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Artificial intelligence was founded as an academic discipline in 1956, and the field went through multiple cycles of optimism throughout its history, followed by periods of disappointment and loss of funding, known as AI winters. Funding and interest vastly increased after 2012 when deep learning outperformed previous AI techniques. This growth accelerated further after 2017 with the transformer architecture, and by the early 2020s many billions of dollars were being invested in AI and the field experienced rapid ongoing progress in what has become known as the AI boom. The emergence of advanced generative AI in the midst of the AI boom and its ability to create and modify content exposed several unintended consequences and harms in the present and raised concerns about the risks of AI and its long-term effects in the future, prompting discussions about regulatory policies to ensure the safety and benefits of the technology.
Goals
The general problem of simulating (or creating) intelligence has been broken into subproblems. These consist of particular traits or capabilities that researchers expect an intelligent system to display. The traits described below have received the most attention and cover the scope of AI research.
Reasoning and problem-solving
Early researchers developed algorithms that imitated step-by-step reasoning that humans use when they solve puzzles or make logical deductions. By the late 1980s and 1990s, methods were developed for dealing with uncertain or incomplete information, employing concepts from probability and economics.
Many of these algorithms are insufficient for solving large reasoning problems because they experience a "combinatorial explosion": They become exponentially slower as the problems grow. Even humans rarely use the step-by-step deduction that early AI research could model. They solve most of their problems using fast, intuitive judgments. Accurate and efficient reasoning is an unsolved problem.
Knowledge representation
Knowledge representation and knowledge engineering allow AI programs to answer questions intelligently and make deductions about real-world facts. Formal knowledge representations are used in content-based indexing and retrieval, scene interpretation, clinical decision support, knowledge discovery (mining "interesting" and actionable inferences from large databases), and other areas. | Artificial intelligence | Wikipedia | 420 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
A knowledge base is a body of knowledge represented in a form that can be used by a program. An ontology is the set of objects, relations, concepts, and properties used by a particular domain of knowledge. Knowledge bases need to represent things such as objects, properties, categories, and relations between objects; situations, events, states, and time; causes and effects; knowledge about knowledge (what we know about what other people know); default reasoning (things that humans assume are true until they are told differently and will remain true even when other facts are changing); and many other aspects and domains of knowledge.
Among the most difficult problems in knowledge representation are the breadth of commonsense knowledge (the set of atomic facts that the average person knows is enormous); and the sub-symbolic form of most commonsense knowledge (much of what people know is not represented as "facts" or "statements" that they could express verbally). There is also the difficulty of knowledge acquisition, the problem of obtaining knowledge for AI applications.
Planning and decision-making
An "agent" is anything that perceives and takes actions in the world. A rational agent has goals or preferences and takes actions to make them happen. In automated planning, the agent has a specific goal. In automated decision-making, the agent has preferences—there are some situations it would prefer to be in, and some situations it is trying to avoid. The decision-making agent assigns a number to each situation (called the "utility") that measures how much the agent prefers it. For each possible action, it can calculate the "expected utility": the utility of all possible outcomes of the action, weighted by the probability that the outcome will occur. It can then choose the action with the maximum expected utility.
In classical planning, the agent knows exactly what the effect of any action will be. In most real-world problems, however, the agent may not be certain about the situation they are in (it is "unknown" or "unobservable") and it may not know for certain what will happen after each possible action (it is not "deterministic"). It must choose an action by making a probabilistic guess and then reassess the situation to see if the action worked. | Artificial intelligence | Wikipedia | 463 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
In some problems, the agent's preferences may be uncertain, especially if there are other agents or humans involved. These can be learned (e.g., with inverse reinforcement learning), or the agent can seek information to improve its preferences. Information value theory can be used to weigh the value of exploratory or experimental actions. The space of possible future actions and situations is typically intractably large, so the agents must take actions and evaluate situations while being uncertain of what the outcome will be.
A Markov decision process has a transition model that describes the probability that a particular action will change the state in a particular way and a reward function that supplies the utility of each state and the cost of each action. A policy associates a decision with each possible state. The policy could be calculated (e.g., by iteration), be heuristic, or it can be learned.
Game theory describes the rational behavior of multiple interacting agents and is used in AI programs that make decisions that involve other agents.
Learning
Machine learning is the study of programs that can improve their performance on a given task automatically. It has been a part of AI from the beginning.
There are several kinds of machine learning. Unsupervised learning analyzes a stream of data and finds patterns and makes predictions without any other guidance. Supervised learning requires labeling the training data with the expected answers, and comes in two main varieties: classification (where the program must learn to predict what category the input belongs in) and regression (where the program must deduce a numeric function based on numeric input).
In reinforcement learning, the agent is rewarded for good responses and punished for bad ones. The agent learns to choose responses that are classified as "good". Transfer learning is when the knowledge gained from one problem is applied to a new problem. Deep learning is a type of machine learning that runs inputs through biologically inspired artificial neural networks for all of these types of learning.
Computational learning theory can assess learners by computational complexity, by sample complexity (how much data is required), or by other notions of optimization.
Natural language processing
Natural language processing (NLP) allows programs to read, write and communicate in human languages such as English. Specific problems include speech recognition, speech synthesis, machine translation, information extraction, information retrieval and question answering. | Artificial intelligence | Wikipedia | 471 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Early work, based on Noam Chomsky's generative grammar and semantic networks, had difficulty with word-sense disambiguation unless restricted to small domains called "micro-worlds" (due to the common sense knowledge problem). Margaret Masterman believed that it was meaning and not grammar that was the key to understanding languages, and that thesauri and not dictionaries should be the basis of computational language structure.
Modern deep learning techniques for NLP include word embedding (representing words, typically as vectors encoding their meaning), transformers (a deep learning architecture using an attention mechanism), and others. In 2019, generative pre-trained transformer (or "GPT") language models began to generate coherent text, and by 2023, these models were able to get human-level scores on the bar exam, SAT test, GRE test, and many other real-world applications.
Perception
Machine perception is the ability to use input from sensors (such as cameras, microphones, wireless signals, active lidar, sonar, radar, and tactile sensors) to deduce aspects of the world. Computer vision is the ability to analyze visual input.
The field includes speech recognition, image classification, facial recognition, object recognition,object tracking, and robotic perception.
Social intelligence
Affective computing is a field that comprises systems that recognize, interpret, process, or simulate human feeling, emotion, and mood. For example, some virtual assistants are programmed to speak conversationally or even to banter humorously; it makes them appear more sensitive to the emotional dynamics of human interaction, or to otherwise facilitate human–computer interaction.
However, this tends to give naïve users an unrealistic conception of the intelligence of existing computer agents. Moderate successes related to affective computing include textual sentiment analysis and, more recently, multimodal sentiment analysis, wherein AI classifies the effects displayed by a videotaped subject.
General intelligence
A machine with artificial general intelligence should be able to solve a wide variety of problems with breadth and versatility similar to human intelligence.
Techniques
AI research uses a wide variety of techniques to accomplish the goals above.
Search and optimization
AI can solve many problems by intelligently searching through many possible solutions. There are two very different kinds of search used in AI: state space search and local search. | Artificial intelligence | Wikipedia | 472 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
State space search
State space search searches through a tree of possible states to try to find a goal state. For example, planning algorithms search through trees of goals and subgoals, attempting to find a path to a target goal, a process called means-ends analysis.
Simple exhaustive searches are rarely sufficient for most real-world problems: the search space (the number of places to search) quickly grows to astronomical numbers. The result is a search that is too slow or never completes. "Heuristics" or "rules of thumb" can help prioritize choices that are more likely to reach a goal.
Adversarial search is used for game-playing programs, such as chess or Go. It searches through a tree of possible moves and countermoves, looking for a winning position.
Local search
Local search uses mathematical optimization to find a solution to a problem. It begins with some form of guess and refines it incrementally.
Gradient descent is a type of local search that optimizes a set of numerical parameters by incrementally adjusting them to minimize a loss function. Variants of gradient descent are commonly used to train neural networks, through the backpropagation algorithm.
Another type of local search is evolutionary computation, which aims to iteratively improve a set of candidate solutions by "mutating" and "recombining" them, selecting only the fittest to survive each generation.
Distributed search processes can coordinate via swarm intelligence algorithms. Two popular swarm algorithms used in search are particle swarm optimization (inspired by bird flocking) and ant colony optimization (inspired by ant trails).
Logic
Formal logic is used for reasoning and knowledge representation.
Formal logic comes in two main forms: propositional logic (which operates on statements that are true or false and uses logical connectives such as "and", "or", "not" and "implies") and predicate logic (which also operates on objects, predicates and relations and uses quantifiers such as "Every X is a Y" and "There are some Xs that are Ys").
Deductive reasoning in logic is the process of proving a new statement (conclusion) from other statements that are given and assumed to be true (the premises). Proofs can be structured as proof trees, in which nodes are labelled by sentences, and children nodes are connected to parent nodes by inference rules. | Artificial intelligence | Wikipedia | 490 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Given a problem and a set of premises, problem-solving reduces to searching for a proof tree whose root node is labelled by a solution of the problem and whose leaf nodes are labelled by premises or axioms. In the case of Horn clauses, problem-solving search can be performed by reasoning forwards from the premises or backwards from the problem. In the more general case of the clausal form of first-order logic, resolution is a single, axiom-free rule of inference, in which a problem is solved by proving a contradiction from premises that include the negation of the problem to be solved.
Inference in both Horn clause logic and first-order logic is undecidable, and therefore intractable. However, backward reasoning with Horn clauses, which underpins computation in the logic programming language Prolog, is Turing complete. Moreover, its efficiency is competitive with computation in other symbolic programming languages.
Fuzzy logic assigns a "degree of truth" between 0 and 1. It can therefore handle propositions that are vague and partially true.
Non-monotonic logics, including logic programming with negation as failure, are designed to handle default reasoning. Other specialized versions of logic have been developed to describe many complex domains.
Probabilistic methods for uncertain reasoning
Many problems in AI (including in reasoning, planning, learning, perception, and robotics) require the agent to operate with incomplete or uncertain information. AI researchers have devised a number of tools to solve these problems using methods from probability theory and economics. Precise mathematical tools have been developed that analyze how an agent can make choices and plan, using decision theory, decision analysis, and information value theory. These tools include models such as Markov decision processes, dynamic decision networks, game theory and mechanism design.
Bayesian networks are a tool that can be used for reasoning (using the Bayesian inference algorithm), learning (using the expectation–maximization algorithm), planning (using decision networks) and perception (using dynamic Bayesian networks).
Probabilistic algorithms can also be used for filtering, prediction, smoothing, and finding explanations for streams of data, thus helping perception systems analyze processes that occur over time (e.g., hidden Markov models or Kalman filters). | Artificial intelligence | Wikipedia | 450 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Classifiers and statistical learning methods
The simplest AI applications can be divided into two types: classifiers (e.g., "if shiny then diamond"), on one hand, and controllers (e.g., "if diamond then pick up"), on the other hand. Classifiers are functions that use pattern matching to determine the closest match. They can be fine-tuned based on chosen examples using supervised learning. Each pattern (also called an "observation") is labeled with a certain predefined class. All the observations combined with their class labels are known as a data set. When a new observation is received, that observation is classified based on previous experience.
There are many kinds of classifiers in use. The decision tree is the simplest and most widely used symbolic machine learning algorithm. K-nearest neighbor algorithm was the most widely used analogical AI until the mid-1990s, and Kernel methods such as the support vector machine (SVM) displaced k-nearest neighbor in the 1990s.
The naive Bayes classifier is reportedly the "most widely used learner" at Google, due in part to its scalability.
Neural networks are also used as classifiers.
Artificial neural networks
An artificial neural network is based on a collection of nodes also known as artificial neurons, which loosely model the neurons in a biological brain. It is trained to recognise patterns; once trained, it can recognise those patterns in fresh data. There is an input, at least one hidden layer of nodes and an output. Each node applies a function and once the weight crosses its specified threshold, the data is transmitted to the next layer. A network is typically called a deep neural network if it has at least 2 hidden layers.
Learning algorithms for neural networks use local search to choose the weights that will get the right output for each input during training. The most common training technique is the backpropagation algorithm. Neural networks learn to model complex relationships between inputs and outputs and find patterns in data. In theory, a neural network can learn any function. | Artificial intelligence | Wikipedia | 412 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
In feedforward neural networks the signal passes in only one direction. Recurrent neural networks feed the output signal back into the input, which allows short-term memories of previous input events. Long short term memory is the most successful network architecture for recurrent networks. Perceptrons use only a single layer of neurons; deep learning uses multiple layers. Convolutional neural networks strengthen the connection between neurons that are "close" to each other—this is especially important in image processing, where a local set of neurons must identify an "edge" before the network can identify an object.
Deep learning
Deep learning uses several layers of neurons between the network's inputs and outputs. The multiple layers can progressively extract higher-level features from the raw input. For example, in image processing, lower layers may identify edges, while higher layers may identify the concepts relevant to a human such as digits, letters, or faces.
Deep learning has profoundly improved the performance of programs in many important subfields of artificial intelligence, including computer vision, speech recognition, natural language processing, image classification, and others. The reason that deep learning performs so well in so many applications is not known as of 2023. The sudden success of deep learning in 2012–2015 did not occur because of some new discovery or theoretical breakthrough (deep neural networks and backpropagation had been described by many people, as far back as the 1950s) but because of two factors: the incredible increase in computer power (including the hundred-fold increase in speed by switching to GPUs) and the availability of vast amounts of training data, especially the giant curated datasets used for benchmark testing, such as ImageNet. | Artificial intelligence | Wikipedia | 340 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
GPT
Generative pre-trained transformers (GPT) are large language models (LLMs) that generate text based on the semantic relationships between words in sentences. Text-based GPT models are pretrained on a large corpus of text that can be from the Internet. The pretraining consists of predicting the next token (a token being usually a word, subword, or punctuation). Throughout this pretraining, GPT models accumulate knowledge about the world and can then generate human-like text by repeatedly predicting the next token. Typically, a subsequent training phase makes the model more truthful, useful, and harmless, usually with a technique called reinforcement learning from human feedback (RLHF). Current GPT models are prone to generating falsehoods called "hallucinations", although this can be reduced with RLHF and quality data. They are used in chatbots, which allow people to ask a question or request a task in simple text.
Current models and services include Gemini (formerly Bard), ChatGPT, Grok, Claude, Copilot, and LLaMA. Multimodal GPT models can process different types of data (modalities) such as images, videos, sound, and text.
Hardware and software
In the late 2010s, graphics processing units (GPUs) that were increasingly designed with AI-specific enhancements and used with specialized TensorFlow software had replaced previously used central processing unit (CPUs) as the dominant means for large-scale (commercial and academic) machine learning models' training. Specialized programming languages such as Prolog were used in early AI research, but general-purpose programming languages like Python have become predominant.
The transistor density in integrated circuits has been observed to roughly double every 18 months—a trend known as Moore's law, named after the Intel co-founder Gordon Moore, who first identified it. Improvements in GPUs have been even faster, a trend sometimes called Huang's law, named after Nvidia co-founder and CEO Jensen Huang. | Artificial intelligence | Wikipedia | 418 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Applications
AI and machine learning technology is used in most of the essential applications of the 2020s, including: search engines (such as Google Search), targeting online advertisements, recommendation systems (offered by Netflix, YouTube or Amazon), driving internet traffic, targeted advertising (AdSense, Facebook), virtual assistants (such as Siri or Alexa), autonomous vehicles (including drones, ADAS and self-driving cars), automatic language translation (Microsoft Translator, Google Translate), facial recognition (Apple's Face ID or Microsoft's DeepFace and Google's FaceNet) and image labeling (used by Facebook, Apple's iPhoto and TikTok). The deployment of AI may be overseen by a Chief automation officer (CAO).
Health and medicine
The application of AI in medicine and medical research has the potential to increase patient care and quality of life. Through the lens of the Hippocratic Oath, medical professionals are ethically compelled to use AI, if applications can more accurately diagnose and treat patients.
For medical research, AI is an important tool for processing and integrating big data. This is particularly important for organoid and tissue engineering development which use microscopy imaging as a key technique in fabrication. It has been suggested that AI can overcome discrepancies in funding allocated to different fields of research. New AI tools can deepen the understanding of biomedically relevant pathways. For example, AlphaFold 2 (2021) demonstrated the ability to approximate, in hours rather than months, the 3D structure of a protein. In 2023, it was reported that AI-guided drug discovery helped find a class of antibiotics capable of killing two different types of drug-resistant bacteria. In 2024, researchers used machine learning to accelerate the search for Parkinson's disease drug treatments. Their aim was to identify compounds that block the clumping, or aggregation, of alpha-synuclein (the protein that characterises Parkinson's disease). They were able to speed up the initial screening process ten-fold and reduce the cost by a thousand-fold.
Sexuality | Artificial intelligence | Wikipedia | 419 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Applications of AI in this domain include AI-enabled menstruation and fertility trackers that analyze user data to offer prediction, AI-integrated sex toys (e.g., teledildonics), AI-generated sexual education content, and AI agents that simulate sexual and romantic partners (e.g., Replika). AI is also used for the production of non-consensual deepfake pornography, raising significant ethical and legal concerns.
AI technologies have also been used to attempt to identify online gender-based violence and online sexual grooming of minors.
Games
Game playing programs have been used since the 1950s to demonstrate and test AI's most advanced techniques. Deep Blue became the first computer chess-playing system to beat a reigning world chess champion, Garry Kasparov, on 11 May 1997. In 2011, in a Jeopardy! quiz show exhibition match, IBM's question answering system, Watson, defeated the two greatest Jeopardy! champions, Brad Rutter and Ken Jennings, by a significant margin. In March 2016, AlphaGo won 4 out of 5 games of Go in a match with Go champion Lee Sedol, becoming the first computer Go-playing system to beat a professional Go player without handicaps. Then, in 2017, it defeated Ke Jie, who was the best Go player in the world. Other programs handle imperfect-information games, such as the poker-playing program Pluribus. DeepMind developed increasingly generalistic reinforcement learning models, such as with MuZero, which could be trained to play chess, Go, or Atari games. In 2019, DeepMind's AlphaStar achieved grandmaster level in StarCraft II, a particularly challenging real-time strategy game that involves incomplete knowledge of what happens on the map. In 2021, an AI agent competed in a PlayStation Gran Turismo competition, winning against four of the world's best Gran Turismo drivers using deep reinforcement learning. In 2024, Google DeepMind introduced SIMA, a type of AI capable of autonomously playing nine previously unseen open-world video games by observing screen output, as well as executing short, specific tasks in response to natural language instructions. | Artificial intelligence | Wikipedia | 441 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Mathematics
In mathematics, special forms of formal step-by-step reasoning are used. In contrast, LLMs such as GPT-4 Turbo, Gemini Ultra, Claude Opus, LLaMa-2 or Mistral Large are working with probabilistic models, which can produce wrong answers in the form of hallucinations. Therefore, they need not only a large database of mathematical problems to learn from but also methods such as supervised fine-tuning or trained classifiers with human-annotated data to improve answers for new problems and learn from corrections. A 2024 study showed that the performance of some language models for reasoning capabilities in solving math problems not included in their training data was low, even for problems with only minor deviations from trained data.
Alternatively, dedicated models for mathematical problem solving with higher precision for the outcome including proof of theorems have been developed such as Alpha Tensor, Alpha Geometry and Alpha Proof all from Google DeepMind, Llemma from eleuther or Julius.
When natural language is used to describe mathematical problems, converters transform such prompts into a formal language such as Lean to define mathematical tasks.
Some models have been developed to solve challenging problems and reach good results in benchmark tests, others to serve as educational tools in mathematics.
Finance
Finance is one of the fastest growing sectors where applied AI tools are being deployed: from retail online banking to investment advice and insurance, where automated "robot advisers" have been in use for some years.
World Pensions experts like Nicolas Firzli insist it may be too early to see the emergence of highly innovative AI-informed financial products and services: "the deployment of AI tools will simply further automatise things: destroying tens of thousands of jobs in banking, financial planning, and pension advice in the process, but I'm not sure it will unleash a new wave of [e.g., sophisticated] pension innovation."
Military
Various countries are deploying AI military applications. The main applications enhance command and control, communications, sensors, integration and interoperability. Research is targeting intelligence collection and analysis, logistics, cyber operations, information operations, and semiautonomous and autonomous vehicles. AI technologies enable coordination of sensors and effectors, threat detection and identification, marking of enemy positions, target acquisition, coordination and deconfliction of distributed Joint Fires between networked combat vehicles involving manned and unmanned teams.
AI has been used in military operations in Iraq, Syria, Israel and Ukraine.
Generative AI | Artificial intelligence | Wikipedia | 502 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Agents
Artificial intelligent (AI) agents are software entities designed to perceive their environment, make decisions, and take actions autonomously to achieve specific goals. These agents can interact with users, their environment, or other agents. AI agents are used in various applications, including virtual assistants, chatbots, autonomous vehicles, game-playing systems, and industrial robotics. AI agents operate within the constraints of their programming, available computational resources, and hardware limitations. This means they are restricted to performing tasks within their defined scope and have finite memory and processing capabilities. In real-world applications, AI agents often face time constraints for decision-making and action execution. Many AI agents incorporate learning algorithms, enabling them to improve their performance over time through experience or training. Using machine learning, AI agents can adapt to new situations and optimise their behaviour for their designated tasks.
Other industry-specific tasks
There are also thousands of successful AI applications used to solve specific problems for specific industries or institutions. In a 2017 survey, one in five companies reported having incorporated "AI" in some offerings or processes. A few examples are energy storage, medical diagnosis, military logistics, applications that predict the result of judicial decisions, foreign policy, or supply chain management.
AI applications for evacuation and disaster management are growing. AI has been used to investigate if and how people evacuated in large scale and small scale evacuations using historical data from GPS, videos or social media. Further, AI can provide real time information on the real time evacuation conditions.
In agriculture, AI has helped farmers identify areas that need irrigation, fertilization, pesticide treatments or increasing yield. Agronomists use AI to conduct research and development. AI has been used to predict the ripening time for crops such as tomatoes, monitor soil moisture, operate agricultural robots, conduct predictive analytics, classify livestock pig call emotions, automate greenhouses, detect diseases and pests, and save water.
Artificial intelligence is used in astronomy to analyze increasing amounts of available data and applications, mainly for "classification, regression, clustering, forecasting, generation, discovery, and the development of new scientific insights." For example, it is used for discovering exoplanets, forecasting solar activity, and distinguishing between signals and instrumental effects in gravitational wave astronomy. Additionally, it could be used for activities in space, such as space exploration, including the analysis of data from space missions, real-time science decisions of spacecraft, space debris avoidance, and more autonomous operation. | Artificial intelligence | Wikipedia | 500 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
During the 2024 Indian elections, US$50 millions was spent on authorized AI-generated content, notably by creating deepfakes of allied (including sometimes deceased) politicians to better engage with voters, and by translating speeches to various local languages.
Ethics
AI has potential benefits and potential risks. AI may be able to advance science and find solutions for serious problems: Demis Hassabis of DeepMind hopes to "solve intelligence, and then use that to solve everything else". However, as the use of AI has become widespread, several unintended consequences and risks have been identified. In-production systems can sometimes not factor ethics and bias into their AI training processes, especially when the AI algorithms are inherently unexplainable in deep learning.
Risks and harm
Privacy and copyright
Machine learning algorithms require large amounts of data. The techniques used to acquire this data have raised concerns about privacy, surveillance and copyright.
AI-powered devices and services, such as virtual assistants and IoT products, continuously collect personal information, raising concerns about intrusive data gathering and unauthorized access by third parties. The loss of privacy is further exacerbated by AI's ability to process and combine vast amounts of data, potentially leading to a surveillance society where individual activities are constantly monitored and analyzed without adequate safeguards or transparency.
Sensitive user data collected may include online activity records, geolocation data, video, or audio. For example, in order to build speech recognition algorithms, Amazon has recorded millions of private conversations and allowed temporary workers to listen to and transcribe some of them. Opinions about this widespread surveillance range from those who see it as a necessary evil to those for whom it is clearly unethical and a violation of the right to privacy.
AI developers argue that this is the only way to deliver valuable applications and have developed several techniques that attempt to preserve privacy while still obtaining the data, such as data aggregation, de-identification and differential privacy. Since 2016, some privacy experts, such as Cynthia Dwork, have begun to view privacy in terms of fairness. Brian Christian wrote that experts have pivoted "from the question of 'what they know' to the question of 'what they're doing with it'." | Artificial intelligence | Wikipedia | 449 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Generative AI is often trained on unlicensed copyrighted works, including in domains such as images or computer code; the output is then used under the rationale of "fair use". Experts disagree about how well and under what circumstances this rationale will hold up in courts of law; relevant factors may include "the purpose and character of the use of the copyrighted work" and "the effect upon the potential market for the copyrighted work". Website owners who do not wish to have their content scraped can indicate it in a "robots.txt" file. In 2023, leading authors (including John Grisham and Jonathan Franzen) sued AI companies for using their work to train generative AI. Another discussed approach is to envision a separate sui generis system of protection for creations generated by AI to ensure fair attribution and compensation for human authors.
Dominance by tech giants
The commercial AI scene is dominated by Big Tech companies such as Alphabet Inc., Amazon, Apple Inc., Meta Platforms, and Microsoft. Some of these players already own the vast majority of existing cloud infrastructure and computing power from data centers, allowing them to entrench further in the marketplace.
Power needs and environmental impacts
In January 2024, the International Energy Agency (IEA) released Electricity 2024, Analysis and Forecast to 2026, forecasting electric power use. This is the first IEA report to make projections for data centers and power consumption for artificial intelligence and cryptocurrency. The report states that power demand for these uses might double by 2026, with additional electric power usage equal to electricity used by the whole Japanese nation. | Artificial intelligence | Wikipedia | 333 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Prodigious power consumption by AI is responsible for the growth of fossil fuels use, and might delay closings of obsolete, carbon-emitting coal energy facilities. There is a feverish rise in the construction of data centers throughout the US, making large technology firms (e.g., Microsoft, Meta, Google, Amazon) into voracious consumers of electric power. Projected electric consumption is so immense that there is concern that it will be fulfilled no matter the source. A ChatGPT search involves the use of 10 times the electrical energy as a Google search. The large firms are in haste to find power sources – from nuclear energy to geothermal to fusion. The tech firms argue that – in the long view – AI will be eventually kinder to the environment, but they need the energy now. AI makes the power grid more efficient and "intelligent", will assist in the growth of nuclear power, and track overall carbon emissions, according to technology firms.
A 2024 Goldman Sachs Research Paper, AI Data Centers and the Coming US Power Demand Surge, found "US power demand (is) likely to experience growth not seen in a generation...." and forecasts that, by 2030, US data centers will consume 8% of US power, as opposed to 3% in 2022, presaging growth for the electrical power generation industry by a variety of means. Data centers' need for more and more electrical power is such that they might max out the electrical grid. The Big Tech companies counter that AI can be used to maximize the utilization of the grid by all.
In 2024, the Wall Street Journal reported that big AI companies have begun negotiations with the US nuclear power providers to provide electricity to the data centers. In March 2024 Amazon purchased a Pennsylvania nuclear-powered data center for $650 Million (US). Nvidia CEO Jen-Hsun Huang said nuclear power is a good option for the data centers. | Artificial intelligence | Wikipedia | 395 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
In September 2024, Microsoft announced an agreement with Constellation Energy to re-open the Three Mile Island nuclear power plant to provide Microsoft with 100% of all electric power produced by the plant for 20 years. Reopening the plant, which suffered a partial nuclear meltdown of its Unit 2 reactor in 1979, will require Constellation to get through strict regulatory processes which will include extensive safety scrutiny from the US Nuclear Regulatory Commission. If approved (this will be the first ever US re-commissioning of a nuclear plant), over 835 megawatts of power – enough for 800,000 homes – of energy will be produced. The cost for re-opening and upgrading is estimated at $1.6 billion (US) and is dependent on tax breaks for nuclear power contained in the 2022 US Inflation Reduction Act. The US government and the state of Michigan are investing almost $2 billion (US) to reopen the Palisades Nuclear reactor on Lake Michigan. Closed since 2022, the plant is planned to be reopened in October 2025. The Three Mile Island facility will be renamed the Crane Clean Energy Center after Chris Crane, a nuclear proponent and former CEO of Exelon who was responsible for Exelon spinoff of Constellation.
After the last approval in September 2023, Taiwan suspended the approval of data centers north of Taoyuan with a capacity of more than 5 MW in 2024, due to power supply shortages. Taiwan aims to phase out nuclear power by 2025. On the other hand, Singapore imposed a ban on the opening of data centers in 2019 due to electric power, but in 2022, lifted this ban.
Although most nuclear plants in Japan have been shut down after the 2011 Fukushima nuclear accident, according to an October 2024 Bloomberg article in Japanese, cloud gaming services company Ubitus, in which Nvidia has a stake, is looking for land in Japan near nuclear power plant for a new data center for generative AI. Ubitus CEO Wesley Kuo said nuclear power plants are the most efficient, cheap and stable power for AI.
On 1 November 2024, the Federal Energy Regulatory Commission (FERC) rejected an application submitted by Talen Energy for approval to supply some electricity from the nuclear power station Susquehanna to Amazon's data center.
According to the Commission Chairman Willie L. Phillips, it is a burden on the electricity grid as well as a significant cost shifting concern to households and other business sectors.
Misinformation | Artificial intelligence | Wikipedia | 497 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
YouTube, Facebook and others use recommender systems to guide users to more content. These AI programs were given the goal of maximizing user engagement (that is, the only goal was to keep people watching). The AI learned that users tended to choose misinformation, conspiracy theories, and extreme partisan content, and, to keep them watching, the AI recommended more of it. Users also tended to watch more content on the same subject, so the AI led people into filter bubbles where they received multiple versions of the same misinformation. This convinced many users that the misinformation was true, and ultimately undermined trust in institutions, the media and the government. The AI program had correctly learned to maximize its goal, but the result was harmful to society. After the U.S. election in 2016, major technology companies took steps to mitigate the problem .
In 2022, generative AI began to create images, audio, video and text that are indistinguishable from real photographs, recordings, films, or human writing. It is possible for bad actors to use this technology to create massive amounts of misinformation or propaganda. AI pioneer Geoffrey Hinton expressed concern about AI enabling "authoritarian leaders to manipulate their electorates" on a large scale, among other risks.
Algorithmic bias and fairness
Machine learning applications will be biased if they learn from biased data. The developers may not be aware that the bias exists. Bias can be introduced by the way training data is selected and by the way a model is deployed. If a biased algorithm is used to make decisions that can seriously harm people (as it can in medicine, finance, recruitment, housing or policing) then the algorithm may cause discrimination. The field of fairness studies how to prevent harms from algorithmic biases.
On June 28, 2015, Google Photos's new image labeling feature mistakenly identified Jacky Alcine and a friend as "gorillas" because they were black. The system was trained on a dataset that contained very few images of black people, a problem called "sample size disparity". Google "fixed" this problem by preventing the system from labelling anything as a "gorilla". Eight years later, in 2023, Google Photos still could not identify a gorilla, and neither could similar products from Apple, Facebook, Microsoft and Amazon. | Artificial intelligence | Wikipedia | 477 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
COMPAS is a commercial program widely used by U.S. courts to assess the likelihood of a defendant becoming a recidivist. In 2016, Julia Angwin at ProPublica discovered that COMPAS exhibited racial bias, despite the fact that the program was not told the races of the defendants. Although the error rate for both whites and blacks was calibrated equal at exactly 61%, the errors for each race were different—the system consistently overestimated the chance that a black person would re-offend and would underestimate the chance that a white person would not re-offend. In 2017, several researchers showed that it was mathematically impossible for COMPAS to accommodate all possible measures of fairness when the base rates of re-offense were different for whites and blacks in the data.
A program can make biased decisions even if the data does not explicitly mention a problematic feature (such as "race" or "gender"). The feature will correlate with other features (like "address", "shopping history" or "first name"), and the program will make the same decisions based on these features as it would on "race" or "gender". Moritz Hardt said "the most robust fact in this research area is that fairness through blindness doesn't work."
Criticism of COMPAS highlighted that machine learning models are designed to make "predictions" that are only valid if we assume that the future will resemble the past. If they are trained on data that includes the results of racist decisions in the past, machine learning models must predict that racist decisions will be made in the future. If an application then uses these predictions as recommendations, some of these "recommendations" will likely be racist. Thus, machine learning is not well suited to help make decisions in areas where there is hope that the future will be better than the past. It is descriptive rather than prescriptive.
Bias and unfairness may go undetected because the developers are overwhelmingly white and male: among AI engineers, about 4% are black and 20% are women. | Artificial intelligence | Wikipedia | 420 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
There are various conflicting definitions and mathematical models of fairness. These notions depend on ethical assumptions, and are influenced by beliefs about society. One broad category is distributive fairness, which focuses on the outcomes, often identifying groups and seeking to compensate for statistical disparities. Representational fairness tries to ensure that AI systems do not reinforce negative stereotypes or render certain groups invisible. Procedural fairness focuses on the decision process rather than the outcome. The most relevant notions of fairness may depend on the context, notably the type of AI application and the stakeholders. The subjectivity in the notions of bias and fairness makes it difficult for companies to operationalize them. Having access to sensitive attributes such as race or gender is also considered by many AI ethicists to be necessary in order to compensate for biases, but it may conflict with anti-discrimination laws.
At its 2022 Conference on Fairness, Accountability, and Transparency (ACM FAccT 2022), the Association for Computing Machinery, in Seoul, South Korea, presented and published findings that recommend that until AI and robotics systems are demonstrated to be free of bias mistakes, they are unsafe, and the use of self-learning neural networks trained on vast, unregulated sources of flawed internet data should be curtailed.
Lack of transparency
Many AI systems are so complex that their designers cannot explain how they reach their decisions. Particularly with deep neural networks, in which there are a large amount of non-linear relationships between inputs and outputs. But some popular explainability techniques exist.
It is impossible to be certain that a program is operating correctly if no one knows how exactly it works. There have been many cases where a machine learning program passed rigorous tests, but nevertheless learned something different than what the programmers intended. For example, a system that could identify skin diseases better than medical professionals was found to actually have a strong tendency to classify images with a ruler as "cancerous", because pictures of malignancies typically include a ruler to show the scale. Another machine learning system designed to help effectively allocate medical resources was found to classify patients with asthma as being at "low risk" of dying from pneumonia. Having asthma is actually a severe risk factor, but since the patients having asthma would usually get much more medical care, they were relatively unlikely to die according to the training data. The correlation between asthma and low risk of dying from pneumonia was real, but misleading. | Artificial intelligence | Wikipedia | 486 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
People who have been harmed by an algorithm's decision have a right to an explanation. Doctors, for example, are expected to clearly and completely explain to their colleagues the reasoning behind any decision they make. Early drafts of the European Union's General Data Protection Regulation in 2016 included an explicit statement that this right exists. Industry experts noted that this is an unsolved problem with no solution in sight. Regulators argued that nevertheless the harm is real: if the problem has no solution, the tools should not be used.
DARPA established the XAI ("Explainable Artificial Intelligence") program in 2014 to try to solve these problems.
Several approaches aim to address the transparency problem. SHAP enables to visualise the contribution of each feature to the output. LIME can locally approximate a model's outputs with a simpler, interpretable model. Multitask learning provides a large number of outputs in addition to the target classification. These other outputs can help developers deduce what the network has learned. Deconvolution, DeepDream and other generative methods can allow developers to see what different layers of a deep network for computer vision have learned, and produce output that can suggest what the network is learning. For generative pre-trained transformers, Anthropic developed a technique based on dictionary learning that associates patterns of neuron activations with human-understandable concepts.
Bad actors and weaponized AI
Artificial intelligence provides a number of tools that are useful to bad actors, such as authoritarian governments, terrorists, criminals or rogue states.
A lethal autonomous weapon is a machine that locates, selects and engages human targets without human supervision. Widely available AI tools can be used by bad actors to develop inexpensive autonomous weapons and, if produced at scale, they are potentially weapons of mass destruction. Even when used in conventional warfare, they currently cannot reliably choose targets and could potentially kill an innocent person. In 2014, 30 nations (including China) supported a ban on autonomous weapons under the United Nations' Convention on Certain Conventional Weapons, however the United States and others disagreed. By 2015, over fifty countries were reported to be researching battlefield robots. | Artificial intelligence | Wikipedia | 432 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
AI tools make it easier for authoritarian governments to efficiently control their citizens in several ways. Face and voice recognition allow widespread surveillance. Machine learning, operating this data, can classify potential enemies of the state and prevent them from hiding. Recommendation systems can precisely target propaganda and misinformation for maximum effect. Deepfakes and generative AI aid in producing misinformation. Advanced AI can make authoritarian centralized decision making more competitive than liberal and decentralized systems such as markets. It lowers the cost and difficulty of digital warfare and advanced spyware. All these technologies have been available since 2020 or earlier—AI facial recognition systems are already being used for mass surveillance in China.
There many other ways that AI is expected to help bad actors, some of which can not be foreseen. For example, machine-learning AI is able to design tens of thousands of toxic molecules in a matter of hours.
Technological unemployment
Economists have frequently highlighted the risks of redundancies from AI, and speculated about unemployment if there is no adequate social policy for full employment.
In the past, technology has tended to increase rather than reduce total employment, but economists acknowledge that "we're in uncharted territory" with AI. A survey of economists showed disagreement about whether the increasing use of robots and AI will cause a substantial increase in long-term unemployment, but they generally agree that it could be a net benefit if productivity gains are redistributed. Risk estimates vary; for example, in the 2010s, Michael Osborne and Carl Benedikt Frey estimated 47% of U.S. jobs are at "high risk" of potential automation, while an OECD report classified only 9% of U.S. jobs as "high risk". The methodology of speculating about future employment levels has been criticised as lacking evidential foundation, and for implying that technology, rather than social policy, creates unemployment, as opposed to redundancies. In April 2023, it was reported that 70% of the jobs for Chinese video game illustrators had been eliminated by generative artificial intelligence.
Unlike previous waves of automation, many middle-class jobs may be eliminated by artificial intelligence; The Economist stated in 2015 that "the worry that AI could do to white-collar jobs what steam power did to blue-collar ones during the Industrial Revolution" is "worth taking seriously". Jobs at extreme risk range from paralegals to fast food cooks, while job demand is likely to increase for care-related professions ranging from personal healthcare to the clergy. | Artificial intelligence | Wikipedia | 510 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
From the early days of the development of artificial intelligence, there have been arguments, for example, those put forward by Joseph Weizenbaum, about whether tasks that can be done by computers actually should be done by them, given the difference between computers and humans, and between quantitative calculation and qualitative, value-based judgement.
Existential risk
It has been argued AI will become so powerful that humanity may irreversibly lose control of it. This could, as physicist Stephen Hawking stated, "spell the end of the human race". This scenario has been common in science fiction, when a computer or robot suddenly develops a human-like "self-awareness" (or "sentience" or "consciousness") and becomes a malevolent character. These sci-fi scenarios are misleading in several ways.
First, AI does not require human-like sentience to be an existential risk. Modern AI programs are given specific goals and use learning and intelligence to achieve them. Philosopher Nick Bostrom argued that if one gives almost any goal to a sufficiently powerful AI, it may choose to destroy humanity to achieve it (he used the example of a paperclip factory manager). Stuart Russell gives the example of household robot that tries to find a way to kill its owner to prevent it from being unplugged, reasoning that "you can't fetch the coffee if you're dead." In order to be safe for humanity, a superintelligence would have to be genuinely aligned with humanity's morality and values so that it is "fundamentally on our side".
Second, Yuval Noah Harari argues that AI does not require a robot body or physical control to pose an existential risk. The essential parts of civilization are not physical. Things like ideologies, law, government, money and the economy are built on language; they exist because there are stories that billions of people believe. The current prevalence of misinformation suggests that an AI could use language to convince people to believe anything, even to take actions that are destructive.
The opinions amongst experts and industry insiders are mixed, with sizable fractions both concerned and unconcerned by risk from eventual superintelligent AI. Personalities such as Stephen Hawking, Bill Gates, and Elon Musk, as well as AI pioneers such as Yoshua Bengio, Stuart Russell, Demis Hassabis, and Sam Altman, have expressed concerns about existential risk from AI. | Artificial intelligence | Wikipedia | 503 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
In May 2023, Geoffrey Hinton announced his resignation from Google in order to be able to "freely speak out about the risks of AI" without "considering how this impacts Google." He notably mentioned risks of an AI takeover, and stressed that in order to avoid the worst outcomes, establishing safety guidelines will require cooperation among those competing in use of AI.
In 2023, many leading AI experts endorsed the joint statement that "Mitigating the risk of extinction from AI should be a global priority alongside other societal-scale risks such as pandemics and nuclear war".
Some other researchers were more optimistic. AI pioneer Jürgen Schmidhuber did not sign the joint statement, emphasising that in 95% of all cases, AI research is about making "human lives longer and healthier and easier." While the tools that are now being used to improve lives can also be used by bad actors, "they can also be used against the bad actors." Andrew Ng also argued that "it's a mistake to fall for the doomsday hype on AI—and that regulators who do will only benefit vested interests." Yann LeCun "scoffs at his peers' dystopian scenarios of supercharged misinformation and even, eventually, human extinction." In the early 2010s, experts argued that the risks are too distant in the future to warrant research or that humans will be valuable from the perspective of a superintelligent machine. However, after 2016, the study of current and future risks and possible solutions became a serious area of research.
Ethical machines and alignment
Friendly AI are machines that have been designed from the beginning to minimize risks and to make choices that benefit humans. Eliezer Yudkowsky, who coined the term, argues that developing friendly AI should be a higher research priority: it may require a large investment and it must be completed before AI becomes an existential risk.
Machines with intelligence have the potential to use their intelligence to make ethical decisions. The field of machine ethics provides machines with ethical principles and procedures for resolving ethical dilemmas.
The field of machine ethics is also called computational morality,
and was founded at an AAAI symposium in 2005.
Other approaches include Wendell Wallach's "artificial moral agents" and Stuart J. Russell's three principles for developing provably beneficial machines. | Artificial intelligence | Wikipedia | 474 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Open source
Active organizations in the AI open-source community include Hugging Face, Google, EleutherAI and Meta. Various AI models, such as Llama 2, Mistral or Stable Diffusion, have been made open-weight, meaning that their architecture and trained parameters (the "weights") are publicly available. Open-weight models can be freely fine-tuned, which allows companies to specialize them with their own data and for their own use-case. Open-weight models are useful for research and innovation but can also be misused. Since they can be fine-tuned, any built-in security measure, such as objecting to harmful requests, can be trained away until it becomes ineffective. Some researchers warn that future AI models may develop dangerous capabilities (such as the potential to drastically facilitate bioterrorism) and that once released on the Internet, they cannot be deleted everywhere if needed. They recommend pre-release audits and cost-benefit analyses.
Frameworks
Artificial Intelligence projects can have their ethical permissibility tested while designing, developing, and implementing an AI system. An AI framework such as the Care and Act Framework containing the SUM values—developed by the Alan Turing Institute tests projects in four main areas:
Respect the dignity of individual people
Connect with other people sincerely, openly, and inclusively
Care for the wellbeing of everyone
Protect social values, justice, and the public interest
Other developments in ethical frameworks include those decided upon during the Asilomar Conference, the Montreal Declaration for Responsible AI, and the IEEE's Ethics of Autonomous Systems initiative, among others; however, these principles do not go without their criticisms, especially regards to the people chosen contributes to these frameworks.
Promotion of the wellbeing of the people and communities that these technologies affect requires consideration of the social and ethical implications at all stages of AI system design, development and implementation, and collaboration between job roles such as data scientists, product managers, data engineers, domain experts, and delivery managers.
The UK AI Safety Institute released in 2024 a testing toolset called 'Inspect' for AI safety evaluations available under a MIT open-source licence which is freely available on GitHub and can be improved with third-party packages. It can be used to evaluate AI models in a range of areas including core knowledge, ability to reason, and autonomous capabilities.
Regulation | Artificial intelligence | Wikipedia | 476 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
The regulation of artificial intelligence is the development of public sector policies and laws for promoting and regulating AI; it is therefore related to the broader regulation of algorithms. The regulatory and policy landscape for AI is an emerging issue in jurisdictions globally. According to AI Index at Stanford, the annual number of AI-related laws passed in the 127 survey countries jumped from one passed in 2016 to 37 passed in 2022 alone. Between 2016 and 2020, more than 30 countries adopted dedicated strategies for AI. Most EU member states had released national AI strategies, as had Canada, China, India, Japan, Mauritius, the Russian Federation, Saudi Arabia, United Arab Emirates, U.S., and Vietnam. Others were in the process of elaborating their own AI strategy, including Bangladesh, Malaysia and Tunisia. The Global Partnership on Artificial Intelligence was launched in June 2020, stating a need for AI to be developed in accordance with human rights and democratic values, to ensure public confidence and trust in the technology. Henry Kissinger, Eric Schmidt, and Daniel Huttenlocher published a joint statement in November 2021 calling for a government commission to regulate AI. In 2023, OpenAI leaders published recommendations for the governance of superintelligence, which they believe may happen in less than 10 years. In 2023, the United Nations also launched an advisory body to provide recommendations on AI governance; the body comprises technology company executives, governments officials and academics. In 2024, the Council of Europe created the first international legally binding treaty on AI, called the "Framework Convention on Artificial Intelligence and Human Rights, Democracy and the Rule of Law". It was adopted by the European Union, the United States, the United Kingdom, and other signatories.
In a 2022 Ipsos survey, attitudes towards AI varied greatly by country; 78% of Chinese citizens, but only 35% of Americans, agreed that "products and services using AI have more benefits than drawbacks". A 2023 Reuters/Ipsos poll found that 61% of Americans agree, and 22% disagree, that AI poses risks to humanity. In a 2023 Fox News poll, 35% of Americans thought it "very important", and an additional 41% thought it "somewhat important", for the federal government to regulate AI, versus 13% responding "not very important" and 8% responding "not at all important". | Artificial intelligence | Wikipedia | 479 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
In November 2023, the first global AI Safety Summit was held in Bletchley Park in the UK to discuss the near and far term risks of AI and the possibility of mandatory and voluntary regulatory frameworks. 28 countries including the United States, China, and the European Union issued a declaration at the start of the summit, calling for international co-operation to manage the challenges and risks of artificial intelligence. In May 2024 at the AI Seoul Summit, 16 global AI tech companies agreed to safety commitments on the development of AI.
History
The study of mechanical or "formal" reasoning began with philosophers and mathematicians in antiquity. The study of logic led directly to Alan Turing's theory of computation, which suggested that a machine, by shuffling symbols as simple as "0" and "1", could simulate any conceivable form of mathematical reasoning. This, along with concurrent discoveries in cybernetics, information theory and neurobiology, led researchers to consider the possibility of building an "electronic brain". They developed several areas of research that would become part of AI, such as McCullouch and Pitts design for "artificial neurons" in 1943, and Turing's influential 1950 paper 'Computing Machinery and Intelligence', which introduced the Turing test and showed that "machine intelligence" was plausible.
The field of AI research was founded at a workshop at Dartmouth College in 1956. The attendees became the leaders of AI research in the 1960s. They and their students produced programs that the press described as "astonishing": computers were learning checkers strategies, solving word problems in algebra, proving logical theorems and speaking English. Artificial intelligence laboratories were set up at a number of British and U.S. universities in the latter 1950s and early 1960s. | Artificial intelligence | Wikipedia | 353 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Researchers in the 1960s and the 1970s were convinced that their methods would eventually succeed in creating a machine with general intelligence and considered this the goal of their field. In 1965 Herbert Simon predicted, "machines will be capable, within twenty years, of doing any work a man can do". In 1967 Marvin Minsky agreed, writing that "within a generation ... the problem of creating 'artificial intelligence' will substantially be solved". They had, however, underestimated the difficulty of the problem. In 1974, both the U.S. and British governments cut off exploratory research in response to the criticism of Sir James Lighthill and ongoing pressure from the U.S. Congress to fund more productive projects. Minsky's and Papert's book Perceptrons was understood as proving that artificial neural networks would never be useful for solving real-world tasks, thus discrediting the approach altogether. The "AI winter", a period when obtaining funding for AI projects was difficult, followed.
In the early 1980s, AI research was revived by the commercial success of expert systems, a form of AI program that simulated the knowledge and analytical skills of human experts. By 1985, the market for AI had reached over a billion dollars. At the same time, Japan's fifth generation computer project inspired the U.S. and British governments to restore funding for academic research. However, beginning with the collapse of the Lisp Machine market in 1987, AI once again fell into disrepute, and a second, longer-lasting winter began.
Up to this point, most of AI's funding had gone to projects that used high-level symbols to represent mental objects like plans, goals, beliefs, and known facts. In the 1980s, some researchers began to doubt that this approach would be able to imitate all the processes of human cognition, especially perception, robotics, learning and pattern recognition, and began to look into "sub-symbolic" approaches. Rodney Brooks rejected "representation" in general and focussed directly on engineering machines that move and survive. Judea Pearl, Lofti Zadeh, and others developed methods that handled incomplete and uncertain information by making reasonable guesses rather than precise logic. But the most important development was the revival of "connectionism", including neural network research, by Geoffrey Hinton and others. In 1990, Yann LeCun successfully showed that convolutional neural networks can recognize handwritten digits, the first of many successful applications of neural networks. | Artificial intelligence | Wikipedia | 508 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
AI gradually restored its reputation in the late 1990s and early 21st century by exploiting formal mathematical methods and by finding specific solutions to specific problems. This "narrow" and "formal" focus allowed researchers to produce verifiable results and collaborate with other fields (such as statistics, economics and mathematics). By 2000, solutions developed by AI researchers were being widely used, although in the 1990s they were rarely described as "artificial intelligence" (a tendency known as the AI effect).
However, several academic researchers became concerned that AI was no longer pursuing its original goal of creating versatile, fully intelligent machines. Beginning around 2002, they founded the subfield of artificial general intelligence (or "AGI"), which had several well-funded institutions by the 2010s.
Deep learning began to dominate industry benchmarks in 2012 and was adopted throughout the field.
For many specific tasks, other methods were abandoned.
Deep learning's success was based on both hardware improvements (faster computers, graphics processing units, cloud computing) and access to large amounts of data (including curated datasets, such as ImageNet). Deep learning's success led to an enormous increase in interest and funding in AI. The amount of machine learning research (measured by total publications) increased by 50% in the years 2015–2019.
In 2016, issues of fairness and the misuse of technology were catapulted into center stage at machine learning conferences, publications vastly increased, funding became available, and many researchers re-focussed their careers on these issues. The alignment problem became a serious field of academic study. | Artificial intelligence | Wikipedia | 319 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
In the late teens and early 2020s, AGI companies began to deliver programs that created enormous interest. In 2015, AlphaGo, developed by DeepMind, beat the world champion Go player. The program taught only the game's rules and developed a strategy by itself. GPT-3 is a large language model that was released in 2020 by OpenAI and is capable of generating high-quality human-like text. ChatGPT, launched on November 30, 2022, became the fastest-growing consumer software application in history, gaining over 100 million users in two months. It marked what is widely regarded as AI's breakout year, bringing it into the public consciousness. These programs, and others, inspired an aggressive AI boom, where large companies began investing billions of dollars in AI research. According to AI Impacts, about $50 billion annually was invested in "AI" around 2022 in the U.S. alone and about 20% of the new U.S. Computer Science PhD graduates have specialized in "AI". About 800,000 "AI"-related U.S. job openings existed in 2022. According to PitchBook research, 22% of newly funded startups in 2024 claimed to be AI companies.
Philosophy
Philosophical debates have historically sought to determine the nature of intelligence and how to make intelligent machines. Another major focus has been whether machines can be conscious, and the associated ethical implications. Many other topics in philosophy are relevant to AI, such as epistemology and free will. Rapid advancements have intensified public discussions on the philosophy and ethics of AI.
Defining artificial intelligence
Alan Turing wrote in 1950 "I propose to consider the question 'can machines think'?" He advised changing the question from whether a machine "thinks", to "whether or not it is possible for machinery to show intelligent behaviour". He devised the Turing test, which measures the ability of a machine to simulate human conversation. Since we can only observe the behavior of the machine, it does not matter if it is "actually" thinking or literally has a "mind". Turing notes that we can not determine these things about other people but "it is usual to have a polite convention that everyone thinks." | Artificial intelligence | Wikipedia | 447 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Russell and Norvig agree with Turing that intelligence must be defined in terms of external behavior, not internal structure. However, they are critical that the test requires the machine to imitate humans. "Aeronautical engineering texts", they wrote, "do not define the goal of their field as making 'machines that fly so exactly like pigeons that they can fool other pigeons. AI founder John McCarthy agreed, writing that "Artificial intelligence is not, by definition, simulation of human intelligence".
McCarthy defines intelligence as "the computational part of the ability to achieve goals in the world". Another AI founder, Marvin Minsky, similarly describes it as "the ability to solve hard problems". The leading AI textbook defines it as the study of agents that perceive their environment and take actions that maximize their chances of achieving defined goals. These definitions view intelligence in terms of well-defined problems with well-defined solutions, where both the difficulty of the problem and the performance of the program are direct measures of the "intelligence" of the machine—and no other philosophical discussion is required, or may not even be possible.
Another definition has been adopted by Google, a major practitioner in the field of AI. This definition stipulates the ability of systems to synthesize information as the manifestation of intelligence, similar to the way it is defined in biological intelligence.
Some authors have suggested in practice, that the definition of AI is vague and difficult to define, with contention as to whether classical algorithms should be categorised as AI, with many companies during the early 2020s AI boom using the term as a marketing buzzword, often even if they did "not actually use AI in a material way".
Evaluating approaches to AI
No established unifying theory or paradigm has guided AI research for most of its history. The unprecedented success of statistical machine learning in the 2010s eclipsed all other approaches (so much so that some sources, especially in the business world, use the term "artificial intelligence" to mean "machine learning with neural networks"). This approach is mostly sub-symbolic, soft and narrow. Critics argue that these questions may have to be revisited by future generations of AI researchers. | Artificial intelligence | Wikipedia | 436 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Symbolic AI and its limits
Symbolic AI (or "GOFAI") simulated the high-level conscious reasoning that people use when they solve puzzles, express legal reasoning and do mathematics. They were highly successful at "intelligent" tasks such as algebra or IQ tests. In the 1960s, Newell and Simon proposed the physical symbol systems hypothesis: "A physical symbol system has the necessary and sufficient means of general intelligent action."
However, the symbolic approach failed on many tasks that humans solve easily, such as learning, recognizing an object or commonsense reasoning. Moravec's paradox is the discovery that high-level "intelligent" tasks were easy for AI, but low level "instinctive" tasks were extremely difficult. Philosopher Hubert Dreyfus had argued since the 1960s that human expertise depends on unconscious instinct rather than conscious symbol manipulation, and on having a "feel" for the situation, rather than explicit symbolic knowledge. Although his arguments had been ridiculed and ignored when they were first presented, eventually, AI research came to agree with him.
The issue is not resolved: sub-symbolic reasoning can make many of the same inscrutable mistakes that human intuition does, such as algorithmic bias. Critics such as Noam Chomsky argue continuing research into symbolic AI will still be necessary to attain general intelligence, in part because sub-symbolic AI is a move away from explainable AI: it can be difficult or impossible to understand why a modern statistical AI program made a particular decision. The emerging field of neuro-symbolic artificial intelligence attempts to bridge the two approaches.
Neat vs. scruffy
"Neats" hope that intelligent behavior is described using simple, elegant principles (such as logic, optimization, or neural networks). "Scruffies" expect that it necessarily requires solving a large number of unrelated problems. Neats defend their programs with theoretical rigor, scruffies rely mainly on incremental testing to see if they work. This issue was actively discussed in the 1970s and 1980s, but eventually was seen as irrelevant. Modern AI has elements of both.
Soft vs. hard computing
Finding a provably correct or optimal solution is intractable for many important problems. Soft computing is a set of techniques, including genetic algorithms, fuzzy logic and neural networks, that are tolerant of imprecision, uncertainty, partial truth and approximation. Soft computing was introduced in the late 1980s and most successful AI programs in the 21st century are examples of soft computing with neural networks.
Narrow vs. general AI | Artificial intelligence | Wikipedia | 504 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
AI researchers are divided as to whether to pursue the goals of artificial general intelligence and superintelligence directly or to solve as many specific problems as possible (narrow AI) in hopes these solutions will lead indirectly to the field's long-term goals. General intelligence is difficult to define and difficult to measure, and modern AI has had more verifiable successes by focusing on specific problems with specific solutions. The sub-field of artificial general intelligence studies this area exclusively.
Machine consciousness, sentience, and mind
The philosophy of mind does not know whether a machine can have a mind, consciousness and mental states, in the same sense that human beings do. This issue considers the internal experiences of the machine, rather than its external behavior. Mainstream AI research considers this issue irrelevant because it does not affect the goals of the field: to build machines that can solve problems using intelligence. Russell and Norvig add that "[t]he additional project of making a machine conscious in exactly the way humans are is not one that we are equipped to take on." However, the question has become central to the philosophy of mind. It is also typically the central question at issue in artificial intelligence in fiction.
Consciousness
David Chalmers identified two problems in understanding the mind, which he named the "hard" and "easy" problems of consciousness. The easy problem is understanding how the brain processes signals, makes plans and controls behavior. The hard problem is explaining how this feels or why it should feel like anything at all, assuming we are right in thinking that it truly does feel like something (Dennett's consciousness illusionism says this is an illusion). While human information processing is easy to explain, human subjective experience is difficult to explain. For example, it is easy to imagine a color-blind person who has learned to identify which objects in their field of view are red, but it is not clear what would be required for the person to know what red looks like.
Computationalism and functionalism
Computationalism is the position in the philosophy of mind that the human mind is an information processing system and that thinking is a form of computing. Computationalism argues that the relationship between mind and body is similar or identical to the relationship between software and hardware and thus may be a solution to the mind–body problem. This philosophical position was inspired by the work of AI researchers and cognitive scientists in the 1960s and was originally proposed by philosophers Jerry Fodor and Hilary Putnam. | Artificial intelligence | Wikipedia | 492 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Philosopher John Searle characterized this position as "strong AI": "The appropriately programmed computer with the right inputs and outputs would thereby have a mind in exactly the same sense human beings have minds." Searle challenges this claim with his Chinese room argument, which attempts to show that even a computer capable of perfectly simulating human behavior would not have a mind.
AI welfare and rights
It is difficult or impossible to reliably evaluate whether an advanced AI is sentient (has the ability to feel), and if so, to what degree. But if there is a significant chance that a given machine can feel and suffer, then it may be entitled to certain rights or welfare protection measures, similarly to animals. Sapience (a set of capacities related to high intelligence, such as discernment or self-awareness) may provide another moral basis for AI rights. Robot rights are also sometimes proposed as a practical way to integrate autonomous agents into society.
In 2017, the European Union considered granting "electronic personhood" to some of the most capable AI systems. Similarly to the legal status of companies, it would have conferred rights but also responsibilities. Critics argued in 2018 that granting rights to AI systems would downplay the importance of human rights, and that legislation should focus on user needs rather than speculative futuristic scenarios. They also noted that robots lacked the autonomy to take part to society on their own.
Progress in AI increased interest in the topic. Proponents of AI welfare and rights often argue that AI sentience, if it emerges, would be particularly easy to deny. They warn that this may be a moral blind spot analogous to slavery or factory farming, which could lead to large-scale suffering if sentient AI is created and carelessly exploited.
Future
Superintelligence and the singularity
A superintelligence is a hypothetical agent that would possess intelligence far surpassing that of the brightest and most gifted human mind. If research into artificial general intelligence produced sufficiently intelligent software, it might be able to reprogram and improve itself. The improved software would be even better at improving itself, leading to what I. J. Good called an "intelligence explosion" and Vernor Vinge called a "singularity".
However, technologies cannot improve exponentially indefinitely, and typically follow an S-shaped curve, slowing when they reach the physical limits of what the technology can do.
Transhumanism | Artificial intelligence | Wikipedia | 479 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Robot designer Hans Moravec, cyberneticist Kevin Warwick and inventor Ray Kurzweil have predicted that humans and machines may merge in the future into cyborgs that are more capable and powerful than either. This idea, called transhumanism, has roots in the writings of Aldous Huxley and Robert Ettinger.
Edward Fredkin argues that "artificial intelligence is the next step in evolution", an idea first proposed by Samuel Butler's "Darwin among the Machines" as far back as 1863, and expanded upon by George Dyson in his 1998 book Darwin Among the Machines: The Evolution of Global Intelligence.
Decomputing
Arguments for decomputing have been raised by Dan McQuillan (Resisting AI: An Anti-fascist Approach to Artificial Intelligence, 2022), meaning an opposition to the sweeping application and expansion of artificial intelligence. Similar to degrowth the approach criticizes AI as an outgrowth of the systemic issues and capitalist world we live in. Arguing that a different future is possible, in which distance between people is reduced and not increased to AI intermediaries.
In fiction
Thought-capable artificial beings have appeared as storytelling devices since antiquity, and have been a persistent theme in science fiction.
A common trope in these works began with Mary Shelley's Frankenstein, where a human creation becomes a threat to its masters. This includes such works as Arthur C. Clarke's and Stanley Kubrick's 2001: A Space Odyssey (both 1968), with HAL 9000, the murderous computer in charge of the Discovery One spaceship, as well as The Terminator (1984) and The Matrix (1999). In contrast, the rare loyal robots such as Gort from The Day the Earth Stood Still (1951) and Bishop from Aliens (1986) are less prominent in popular culture.
Isaac Asimov introduced the Three Laws of Robotics in many stories, most notably with the "Multivac" super-intelligent computer. Asimov's laws are often brought up during lay discussions of machine ethics; while almost all artificial intelligence researchers are familiar with Asimov's laws through popular culture, they generally consider the laws useless for many reasons, one of which is their ambiguity. | Artificial intelligence | Wikipedia | 444 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Several works use AI to force us to confront the fundamental question of what makes us human, showing us artificial beings that have the ability to feel, and thus to suffer. This appears in Karel Čapek's R.U.R., the films A.I. Artificial Intelligence and Ex Machina, as well as the novel Do Androids Dream of Electric Sheep?, by Philip K. Dick. Dick considers the idea that our understanding of human subjectivity is altered by technology created with artificial intelligence. | Artificial intelligence | Wikipedia | 102 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
In mathematics, a binary relation on a set is antisymmetric if there is no pair of distinct elements of each of which is related by to the other. More formally, is antisymmetric precisely if for all
or equivalently,
The definition of antisymmetry says nothing about whether actually holds or not for any . An antisymmetric relation on a set may be reflexive (that is, for all ), irreflexive (that is, for no ), or neither reflexive nor irreflexive. A relation is asymmetric if and only if it is both antisymmetric and irreflexive.
Examples
The divisibility relation on the natural numbers is an important example of an antisymmetric relation. In this context, antisymmetry means that the only way each of two numbers can be divisible by the other is if the two are, in fact, the same number; equivalently, if and are distinct and is a factor of then cannot be a factor of For example, 12 is divisible by 4, but 4 is not divisible by 12.
The usual order relation on the real numbers is antisymmetric: if for two real numbers and both inequalities and hold, then and must be equal. Similarly, the subset order on the subsets of any given set is antisymmetric: given two sets and if every element in also is in and every element in is also in then and must contain all the same elements and therefore be equal:
A real-life example of a relation that is typically antisymmetric is "paid the restaurant bill of" (understood as restricted to a given occasion). Typically, some people pay their own bills, while others pay for their spouses or friends. As long as no two people pay each other's bills, the relation is antisymmetric.
Properties
Partial and total orders are antisymmetric by definition. A relation can be both symmetric and antisymmetric (in this case, it must be coreflexive), and there are relations which are neither symmetric nor antisymmetric (for example, the "preys on" relation on biological species).
Antisymmetry is different from asymmetry: a relation is asymmetric if and only if it is antisymmetric and irreflexive. | Antisymmetric relation | Wikipedia | 493 | 1176 | https://en.wikipedia.org/wiki/Antisymmetric%20relation | Mathematics | Order theory | null |
Astrometry is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It provides the kinematics and physical origin of the Solar System and this galaxy, the Milky Way.
History
The history of astrometry is linked to the history of star catalogues, which gave astronomers reference points for objects in the sky so they could track their movements. This can be dated back to the ancient Greek astronomer Hipparchus, who around 190 BC used the catalogue of his predecessors Timocharis and Aristillus to discover Earth's precession. In doing so, he also developed the brightness scale still in use today. Hipparchus compiled a catalogue with at least 850 stars and their positions. Hipparchus's successor, Ptolemy, included a catalogue of 1,022 stars in his work the Almagest, giving their location, coordinates, and brightness.
In the 10th century, the Iranian astronomer Abd al-Rahman al-Sufi carried out observations on the stars and described their positions, magnitudes and star color; furthermore, he provided drawings for each constellation, which are depicted in his Book of Fixed Stars. Egyptian mathematician Ibn Yunus observed more than 10,000 entries for the Sun's position for many years using a large astrolabe with a diameter of nearly 1.4 metres. His observations on eclipses were still used centuries later in Canadian–American astronomer Simon Newcomb's investigations on the motion of the Moon, while his other observations of the motions of the planets Jupiter and Saturn inspired French scholar Laplace's Obliquity of the Ecliptic and Inequalities of Jupiter and Saturn. In the 15th century, the Timurid astronomer Ulugh Beg compiled the Zij-i-Sultani, in which he catalogued 1,019 stars. Like the earlier catalogs of Hipparchus and Ptolemy, Ulugh Beg's catalogue is estimated to have been precise to within approximately 20 minutes of arc.
In the 16th century, Danish astronomer Tycho Brahe used improved instruments, including large mural instruments, to measure star positions more accurately than previously, with a precision of 15–35 arcsec. Ottoman scholar Taqi al-Din measured the right ascension of the stars at the Constantinople Observatory of Taqi ad-Din using the "observational clock" he invented. When telescopes became commonplace, setting circles sped measurements | Astrometry | Wikipedia | 485 | 1181 | https://en.wikipedia.org/wiki/Astrometry | Physical sciences | Astrometry | null |
English astronomer James Bradley first tried to measure stellar parallaxes in 1729. The stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light and the nutation of the Earth's axis. His cataloguing of 3222 stars was refined in 1807 by German astronomer Friedrich Bessel, the father of modern astrometry. He made the first measurement of stellar parallax: 0.3 arcsec for the binary star 61 Cygni. In 1872, British astronomer William Huggins used spectroscopy to measure the radial velocity of several prominent stars, including Sirius.
Being very difficult to measure, only about 60 stellar parallaxes had been obtained by the end of the 19th century, mostly by use of the filar micrometer. Astrographs using astronomical photographic plates sped the process in the early 20th century. Automated plate-measuring machines and more sophisticated computer technology of the 1960s allowed more efficient compilation of star catalogues. Started in the late 19th century, the project Carte du Ciel to improve star mapping could not be finished but made photography a common technique for astrometry. In the 1980s, charge-coupled devices (CCDs) replaced photographic plates and reduced optical uncertainties to one milliarcsecond. This technology made astrometry less expensive, opening the field to an amateur audience. | Astrometry | Wikipedia | 266 | 1181 | https://en.wikipedia.org/wiki/Astrometry | Physical sciences | Astrometry | null |
In 1989, the European Space Agency's Hipparcos satellite took astrometry into orbit, where it could be less affected by mechanical forces of the Earth and optical distortions from its atmosphere. Operated from 1989 to 1993, Hipparcos measured large and small angles on the sky with much greater precision than any previous optical telescopes. During its 4-year run, the positions, parallaxes, and proper motions of 118,218 stars were determined with an unprecedented degree of accuracy. A new "Tycho catalog" drew together a database of 1,058,332 stars to within 20-30 mas (milliarcseconds). Additional catalogues were compiled for the 23,882 double and multiple stars and 11,597 variable stars also analyzed during the Hipparcos mission.
In 2013, the Gaia satellite was launched and improved the accuracy of Hipparcos.
The precision was improved by a factor of 100 and enabled the mapping of a billion stars.
Today, the catalogue most often used is USNO-B1.0, an all-sky catalogue that tracks proper motions, positions, magnitudes and other characteristics for over one billion stellar objects. During the past 50 years, 7,435 Schmidt camera plates were used to complete several sky surveys that make the data in USNO-B1.0 accurate to within 0.2 arcsec.
Applications
Apart from the fundamental function of providing astronomers with a reference frame to report their observations in, astrometry is also fundamental for fields like celestial mechanics, stellar dynamics and galactic astronomy. In observational astronomy, astrometric techniques help identify stellar objects by their unique motions. It is instrumental for keeping time, in that UTC is essentially the atomic time synchronized to Earth's rotation by means of exact astronomical observations. Astrometry is an important step in the cosmic distance ladder because it establishes parallax distance estimates for stars in the Milky Way. | Astrometry | Wikipedia | 383 | 1181 | https://en.wikipedia.org/wiki/Astrometry | Physical sciences | Astrometry | null |
Astrometry has also been used to support claims of extrasolar planet detection by measuring the displacement the proposed planets cause in their parent star's apparent position on the sky, due to their mutual orbit around the center of mass of the system. Astrometry is more accurate in space missions that are not affected by the distorting effects of the Earth's atmosphere. NASA's planned Space Interferometry Mission (SIM PlanetQuest) (now cancelled) was to utilize astrometric techniques to detect terrestrial planets orbiting 200 or so of the nearest solar-type stars. The European Space Agency's Gaia Mission, launched in 2013, applies astrometric techniques in its stellar census. In addition to the detection of exoplanets, it can also be used to determine their mass.
Astrometric measurements are used by astrophysicists to constrain certain models in celestial mechanics. By measuring the velocities of pulsars, it is possible to put a limit on the asymmetry of supernova explosions. Also, astrometric results are used to determine the distribution of dark matter in the galaxy.
Astronomers use astrometric techniques for the tracking of near-Earth objects. Astrometry is responsible for the detection of many record-breaking Solar System objects. To find such objects astrometrically, astronomers use telescopes to survey the sky and large-area cameras to take pictures at various determined intervals. By studying these images, they can detect Solar System objects by their movements relative to the background stars, which remain fixed. Once a movement per unit time is observed, astronomers compensate for the parallax caused by Earth's motion during this time and the heliocentric distance to this object is calculated. Using this distance and other photographs, more information about the object, including its orbital elements, can be obtained. Asteroid impact avoidance is among the purposes.
Quaoar and Sedna are two trans-Neptunian dwarf planets discovered in this way by Michael E. Brown and others at Caltech using the Palomar Observatory's Samuel Oschin telescope of and the Palomar-Quest large-area CCD camera. The ability of astronomers to track the positions and movements of such celestial bodies is crucial to the understanding of the Solar System and its interrelated past, present, and future with others in the Universe.
Statistics | Astrometry | Wikipedia | 470 | 1181 | https://en.wikipedia.org/wiki/Astrometry | Physical sciences | Astrometry | null |
A fundamental aspect of astrometry is error correction. Various factors introduce errors into the measurement of stellar positions, including atmospheric conditions, imperfections in the instruments and errors by the observer or the measuring instruments. Many of these errors can be reduced by various techniques, such as through instrument improvements and compensations to the data. The results are then analyzed using statistical methods to compute data estimates and error ranges.
Computer programs
XParallax viu (Free application for Windows)
Astrometrica (Application for Windows)
Astrometry.net (Online blind astrometry) | Astrometry | Wikipedia | 111 | 1181 | https://en.wikipedia.org/wiki/Astrometry | Physical sciences | Astrometry | null |
An alloy is a mixture of chemical elements of which in most cases at least one is a metallic element, although it is also sometimes used for mixtures of elements; herein only metallic alloys are described. Most alloys are metallic and show good electrical conductivity, ductility, opacity, and luster, and may have properties that differ from those of the pure elements such as increased strength or hardness. In some cases, an alloy may reduce the overall cost of the material while preserving important properties. In other cases, the mixture imparts synergistic properties such as corrosion resistance or mechanical strength.
In an alloy, the atoms are joined by metallic bonding rather than by covalent bonds typically found in chemical compounds. The alloy constituents are usually measured by mass percentage for practical applications, and in atomic fraction for basic science studies. Alloys are usually classified as substitutional or interstitial alloys, depending on the atomic arrangement that forms the alloy. They can be further classified as homogeneous (consisting of a single phase), or heterogeneous (consisting of two or more phases) or intermetallic. An alloy may be a solid solution of metal elements (a single phase, where all metallic grains (crystals) are of the same composition) or a mixture of metallic phases (two or more solutions, forming a microstructure of different crystals within the metal).
Examples of alloys include red gold (gold and copper), white gold (gold and silver), sterling silver (silver and copper), steel or silicon steel (iron with non-metallic carbon or silicon respectively), solder, brass, pewter, duralumin, bronze, and amalgams.
Alloys are used in a wide variety of applications, from the steel alloys, used in everything from buildings to automobiles to surgical tools, to exotic titanium alloys used in the aerospace industry, to beryllium-copper alloys for non-sparking tools.
Characteristics | Alloy | Wikipedia | 393 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
An alloy is a mixture of chemical elements, which forms an impure substance (admixture) that retains the characteristics of a metal. An alloy is distinct from an impure metal in that, with an alloy, the added elements are well controlled to produce desirable properties, while impure metals such as wrought iron are less controlled, but are often considered useful. Alloys are made by mixing two or more elements, at least one of which is a metal. This is usually called the primary metal or the base metal, and the name of this metal may also be the name of the alloy. The other constituents may or may not be metals but, when mixed with the molten base, they will be soluble and dissolve into the mixture.
The mechanical properties of alloys will often be quite different from those of its individual constituents. A metal that is normally very soft (malleable), such as aluminium, can be altered by alloying it with another soft metal, such as copper. Although both metals are very soft and ductile, the resulting aluminium alloy will have much greater strength. Adding a small amount of non-metallic carbon to iron trades its great ductility for the greater strength of an alloy called steel. Due to its very-high strength, but still substantial toughness, and its ability to be greatly altered by heat treatment, steel is one of the most useful and common alloys in modern use. By adding chromium to steel, its resistance to corrosion can be enhanced, creating stainless steel, while adding silicon will alter its electrical characteristics, producing silicon steel. | Alloy | Wikipedia | 316 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
Like oil and water, a molten metal may not always mix with another element. For example, pure iron is almost completely insoluble with copper. Even when the constituents are soluble, each will usually have a saturation point, beyond which no more of the constituent can be added. Iron, for example, can hold a maximum of 6.67% carbon. Although the elements of an alloy usually must be soluble in the liquid state, they may not always be soluble in the solid state. If the metals remain soluble when solid, the alloy forms a solid solution, becoming a homogeneous structure consisting of identical crystals, called a phase. If as the mixture cools the constituents become insoluble, they may separate to form two or more different types of crystals, creating a heterogeneous microstructure of different phases, some with more of one constituent than the other. However, in other alloys, the insoluble elements may not separate until after crystallization occurs. If cooled very quickly, they first crystallize as a homogeneous phase, but they are supersaturated with the secondary constituents. As time passes, the atoms of these supersaturated alloys can separate from the crystal lattice, becoming more stable, and forming a second phase that serves to reinforce the crystals internally. | Alloy | Wikipedia | 264 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
Some alloys, such as electrum—an alloy of silver and gold—occur naturally. Meteorites are sometimes made of naturally occurring alloys of iron and nickel, but are not native to the Earth. One of the first alloys made by humans was bronze, which is a mixture of the metals tin and copper. Bronze was an extremely useful alloy to the ancients, because it is much stronger and harder than either of its components. Steel was another common alloy. However, in ancient times, it could only be created as an accidental byproduct from the heating of iron ore in fires (smelting) during the manufacture of iron. Other ancient alloys include pewter, brass and pig iron. In the modern age, steel can be created in many forms. Carbon steel can be made by varying only the carbon content, producing soft alloys like mild steel or hard alloys like spring steel. Alloy steels can be made by adding other elements, such as chromium, molybdenum, vanadium or nickel, resulting in alloys such as high-speed steel or tool steel. Small amounts of manganese are usually alloyed with most modern steels because of its ability to remove unwanted impurities, like phosphorus, sulfur and oxygen, which can have detrimental effects on the alloy. However, most alloys were not created until the 1900s, such as various aluminium, titanium, nickel, and magnesium alloys. Some modern superalloys, such as incoloy, inconel, and hastelloy, may consist of a multitude of different elements.
An alloy is technically an impure metal, but when referring to alloys, the term impurities usually denotes undesirable elements. Such impurities are introduced from the base metals and alloying elements, but are removed during processing. For instance, sulfur is a common impurity in steel. Sulfur combines readily with iron to form iron sulfide, which is very brittle, creating weak spots in the steel. Lithium, sodium and calcium are common impurities in aluminium alloys, which can have adverse effects on the structural integrity of castings. Conversely, otherwise pure-metals that contain unwanted impurities are often called "impure metals" and are not usually referred to as alloys. Oxygen, present in the air, readily combines with most metals to form metal oxides; especially at higher temperatures encountered during alloying. Great care is often taken during the alloying process to remove excess impurities, using fluxes, chemical additives, or other methods of extractive metallurgy. | Alloy | Wikipedia | 512 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
Theory
Alloying a metal is done by combining it with one or more other elements. The most common and oldest alloying process is performed by heating the base metal beyond its melting point and then dissolving the solutes into the molten liquid, which may be possible even if the melting point of the solute is far greater than that of the base. For example, in its liquid state, titanium is a very strong solvent capable of dissolving most metals and elements. In addition, it readily absorbs gases like oxygen and burns in the presence of nitrogen. This increases the chance of contamination from any contacting surface, and so must be melted in vacuum induction-heating and special, water-cooled, copper crucibles. However, some metals and solutes, such as iron and carbon, have very high melting-points and were impossible for ancient people to melt. Thus, alloying (in particular, interstitial alloying) may also be performed with one or more constituents in a gaseous state, such as found in a blast furnace to make pig iron (liquid-gas), nitriding, carbonitriding or other forms of case hardening (solid-gas), or the cementation process used to make blister steel (solid-gas). It may also be done with one, more, or all of the constituents in the solid state, such as found in ancient methods of pattern welding (solid-solid), shear steel (solid-solid), or crucible steel production (solid-liquid), mixing the elements via solid-state diffusion. | Alloy | Wikipedia | 325 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
By adding another element to a metal, differences in the size of the atoms create internal stresses in the lattice of the metallic crystals; stresses that often enhance its properties. For example, the combination of carbon with iron produces steel, which is stronger than iron, its primary element. The electrical and thermal conductivity of alloys is usually lower than that of the pure metals. The physical properties, such as density, reactivity, Young's modulus of an alloy may not differ greatly from those of its base element, but engineering properties such as tensile strength, ductility, and shear strength may be substantially different from those of the constituent materials. This is sometimes a result of the sizes of the atoms in the alloy, because larger atoms exert a compressive force on neighboring atoms, and smaller atoms exert a tensile force on their neighbors, helping the alloy resist deformation. Sometimes alloys may exhibit marked differences in behavior even when small amounts of one element are present. For example, impurities in semiconducting ferromagnetic alloys lead to different properties, as first predicted by White, Hogan, Suhl, Tian Abrie and Nakamura.
Unlike pure metals, most alloys do not have a single melting point, but a melting range during which the material is a mixture of solid and liquid phases (a slush). The temperature at which melting begins is called the solidus, and the temperature when melting is just complete is called the liquidus. For many alloys there is a particular alloy proportion (in some cases more than one), called either a eutectic mixture or a peritectic composition, which gives the alloy a unique and low melting point, and no liquid/solid slush transition.
Heat treatment
Alloying elements are added to a base metal, to induce hardness, toughness, ductility, or other desired properties. Most metals and alloys can be work hardened by creating defects in their crystal structure. These defects are created during plastic deformation by hammering, bending, extruding, et cetera, and are permanent unless the metal is recrystallized. Otherwise, some alloys can also have their properties altered by heat treatment. Nearly all metals can be softened by annealing, which recrystallizes the alloy and repairs the defects, but not as many can be hardened by controlled heating and cooling. Many alloys of aluminium, copper, magnesium, titanium, and nickel can be strengthened to some degree by some method of heat treatment, but few respond to this to the same degree as does steel. | Alloy | Wikipedia | 510 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
The base metal iron of the iron-carbon alloy known as steel, undergoes a change in the arrangement (allotropy) of the atoms of its crystal matrix at a certain temperature (usually between and , depending on carbon content). This allows the smaller carbon atoms to enter the interstices of the iron crystal. When this diffusion happens, the carbon atoms are said to be in solution in the iron, forming a particular single, homogeneous, crystalline phase called austenite. If the steel is cooled slowly, the carbon can diffuse out of the iron and it will gradually revert to its low temperature allotrope. During slow cooling, the carbon atoms will no longer be as soluble with the iron, and will be forced to precipitate out of solution, nucleating into a more concentrated form of iron carbide (Fe3C) in the spaces between the pure iron crystals. The steel then becomes heterogeneous, as it is formed of two phases, the iron-carbon phase called cementite (or carbide), and pure iron ferrite. Such a heat treatment produces a steel that is rather soft. If the steel is cooled quickly, however, the carbon atoms will not have time to diffuse and precipitate out as carbide, but will be trapped within the iron crystals. When rapidly cooled, a diffusionless (martensite) transformation occurs, in which the carbon atoms become trapped in solution. This causes the iron crystals to deform as the crystal structure tries to change to its low temperature state, leaving those crystals very hard but much less ductile (more brittle).
While the high strength of steel results when diffusion and precipitation is prevented (forming martensite), most heat-treatable alloys are precipitation hardening alloys, that depend on the diffusion of alloying elements to achieve their strength. When heated to form a solution and then cooled quickly, these alloys become much softer than normal, during the diffusionless transformation, but then harden as they age. The solutes in these alloys will precipitate over time, forming intermetallic phases, which are difficult to discern from the base metal. Unlike steel, in which the solid solution separates into different crystal phases (carbide and ferrite), precipitation hardening alloys form different phases within the same crystal. These intermetallic alloys appear homogeneous in crystal structure, but tend to behave heterogeneously, becoming hard and somewhat brittle. | Alloy | Wikipedia | 508 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
In 1906, precipitation hardening alloys were discovered by Alfred Wilm. Precipitation hardening alloys, such as certain alloys of aluminium, titanium, and copper, are heat-treatable alloys that soften when quenched (cooled quickly), and then harden over time. Wilm had been searching for a way to harden aluminium alloys for use in machine-gun cartridge cases. Knowing that aluminium-copper alloys were heat-treatable to some degree, Wilm tried quenching a ternary alloy of aluminium, copper, and the addition of magnesium, but was initially disappointed with the results. However, when Wilm retested it the next day he discovered that the alloy increased in hardness when left to age at room temperature, and far exceeded his expectations. Although an explanation for the phenomenon was not provided until 1919, duralumin was one of the first "age hardening" alloys used, becoming the primary building material for the first Zeppelins, and was soon followed by many others. Because they often exhibit a combination of high strength and low weight, these alloys became widely used in many forms of industry, including the construction of modern aircraft.
Mechanisms
When a molten metal is mixed with another substance, there are two mechanisms that can cause an alloy to form, called atom exchange and the interstitial mechanism. The relative size of each element in the mix plays a primary role in determining which mechanism will occur. When the atoms are relatively similar in size, the atom exchange method usually happens, where some of the atoms composing the metallic crystals are substituted with atoms of the other constituent. This is called a substitutional alloy. Examples of substitutional alloys include bronze and brass, in which some of the copper atoms are substituted with either tin or zinc atoms respectively.
In the case of the interstitial mechanism, one atom is usually much smaller than the other and can not successfully substitute for the other type of atom in the crystals of the base metal. Instead, the smaller atoms become trapped in the interstitial sites between the atoms of the crystal matrix. This is referred to as an interstitial alloy. Steel is an example of an interstitial alloy, because the very small carbon atoms fit into interstices of the iron matrix.
Stainless steel is an example of a combination of interstitial and substitutional alloys, because the carbon atoms fit into the interstices, but some of the iron atoms are substituted by nickel and chromium atoms.
History and examples
Meteoric iron | Alloy | Wikipedia | 501 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
The use of alloys by humans started with the use of meteoric iron, a naturally occurring alloy of nickel and iron. It is the main constituent of iron meteorites. As no metallurgic processes were used to separate iron from nickel, the alloy was used as it was. Meteoric iron could be forged from a red heat to make objects such as tools, weapons, and nails. In many cultures it was shaped by cold hammering into knives and arrowheads. They were often used as anvils. Meteoric iron was very rare and valuable, and difficult for ancient people to work.
Bronze and brass
Iron is usually found as iron ore on Earth, except for one deposit of native iron in Greenland, which was used by the Inuit. Native copper, however, was found worldwide, along with silver, gold, and platinum, which were also used to make tools, jewelry, and other objects since Neolithic times. Copper was the hardest of these metals, and the most widely distributed. It became one of the most important metals to the ancients. Around 10,000 years ago in the highlands of Anatolia (Turkey), humans learned to smelt metals such as copper and tin from ore. Around 2500 BC, people began alloying the two metals to form bronze, which was much harder than its ingredients. Tin was rare, however, being found mostly in Great Britain. In the Middle East, people began alloying copper with zinc to form brass. Ancient civilizations took into account the mixture and the various properties it produced, such as hardness, toughness and melting point, under various conditions of temperature and work hardening, developing much of the information contained in modern alloy phase diagrams. For example, arrowheads from the Chinese Qin dynasty (around 200 BC) were often constructed with a hard bronze-head, but a softer bronze-tang, combining the alloys to prevent both dulling and breaking during use.
Amalgams | Alloy | Wikipedia | 387 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
Mercury has been smelted from cinnabar for thousands of years. Mercury dissolves many metals, such as gold, silver, and tin, to form amalgams (an alloy in a soft paste or liquid form at ambient temperature). Amalgams have been used since 200 BC in China for gilding objects such as armor and mirrors with precious metals. The ancient Romans often used mercury-tin amalgams for gilding their armor. The amalgam was applied as a paste and then heated until the mercury vaporized, leaving the gold, silver, or tin behind. Mercury was often used in mining, to extract precious metals like gold and silver from their ores.
Precious metals
Many ancient civilizations alloyed metals for purely aesthetic purposes. In ancient Egypt and Mycenae, gold was often alloyed with copper to produce red-gold, or iron to produce a bright burgundy-gold. Gold was often found alloyed with silver or other metals to produce various types of colored gold. These metals were also used to strengthen each other, for more practical purposes. Copper was often added to silver to make sterling silver, increasing its strength for use in dishes, silverware, and other practical items. Quite often, precious metals were alloyed with less valuable substances as a means to deceive buyers. Around 250 BC, Archimedes was commissioned by the King of Syracuse to find a way to check the purity of the gold in a crown, leading to the famous bath-house shouting of "Eureka!" upon the discovery of Archimedes' principle.
Pewter
The term pewter covers a variety of alloys consisting primarily of tin. As a pure metal, tin is much too soft to use for most practical purposes. However, during the Bronze Age, tin was a rare metal in many parts of Europe and the Mediterranean, so it was often valued higher than gold. To make jewellery, cutlery, or other objects from tin, workers usually alloyed it with other metals to increase strength and hardness. These metals were typically lead, antimony, bismuth or copper. These solutes were sometimes added individually in varying amounts, or added together, making a wide variety of objects, ranging from practical items such as dishes, surgical tools, candlesticks or funnels, to decorative items like ear rings and hair clips. | Alloy | Wikipedia | 473 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
The earliest examples of pewter come from ancient Egypt, around 1450 BC. The use of pewter was widespread across Europe, from France to Norway and Britain (where most of the ancient tin was mined) to the Near East. The alloy was also used in China and the Far East, arriving in Japan around 800 AD, where it was used for making objects like ceremonial vessels, tea canisters, or chalices used in shinto shrines.
Iron
The first known smelting of iron began in Anatolia, around 1800 BC. Called the bloomery process, it produced very soft but ductile wrought iron. By 800 BC, iron-making technology had spread to Europe, arriving in Japan around 700 AD. Pig iron, a very hard but brittle alloy of iron and carbon, was being produced in China as early as 1200 BC, but did not arrive in Europe until the Middle Ages. Pig iron has a lower melting point than iron, and was used for making cast-iron. However, these metals found little practical use until the introduction of crucible steel around 300 BC. These steels were of poor quality, and the introduction of pattern welding, around the 1st century AD, sought to balance the extreme properties of the alloys by laminating them, to create a tougher metal. Around 700 AD, the Japanese began folding bloomery-steel and cast-iron in alternating layers to increase the strength of their swords, using clay fluxes to remove slag and impurities. This method of Japanese swordsmithing produced one of the purest steel-alloys of the ancient world. | Alloy | Wikipedia | 320 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
While the use of iron started to become more widespread around 1200 BC, mainly because of interruptions in the trade routes for tin, the metal was much softer than bronze. However, very small amounts of steel, (an alloy of iron and around 1% carbon), was always a byproduct of the bloomery process. The ability to modify the hardness of steel by heat treatment had been known since 1100 BC, and the rare material was valued for the manufacture of tools and weapons. Because the ancients could not produce temperatures high enough to melt iron fully, the production of steel in decent quantities did not occur until the introduction of blister steel during the Middle Ages. This method introduced carbon by heating wrought iron in charcoal for long periods of time, but the absorption of carbon in this manner is extremely slow thus the penetration was not very deep, so the alloy was not homogeneous. In 1740, Benjamin Huntsman began melting blister steel in a crucible to even out the carbon content, creating the first process for the mass production of tool steel. Huntsman's process was used for manufacturing tool steel until the early 1900s.
The introduction of the blast furnace to Europe in the Middle Ages meant that people could produce pig iron in much higher volumes than wrought iron. Because pig iron could be melted, people began to develop processes to reduce carbon in liquid pig iron to create steel. Puddling had been used in China since the first century, and was introduced in Europe during the 1700s, where molten pig iron was stirred while exposed to the air, to remove the carbon by oxidation. In 1858, Henry Bessemer developed a process of steel-making by blowing hot air through liquid pig iron to reduce the carbon content. The Bessemer process led to the first large scale manufacture of steel. | Alloy | Wikipedia | 364 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
Steel is an alloy of iron and carbon, but the term alloy steel usually only refers to steels that contain other elements— like vanadium, molybdenum, or cobalt—in amounts sufficient to alter the properties of the base steel. Since ancient times, when steel was used primarily for tools and weapons, the methods of producing and working the metal were often closely guarded secrets. Even long after the Age of Enlightenment, the steel industry was very competitive and manufacturers went through great lengths to keep their processes confidential, resisting any attempts to scientifically analyze the material for fear it would reveal their methods. For example, the people of Sheffield, a center of steel production in England, were known to routinely bar visitors and tourists from entering town to deter industrial espionage. Thus, almost no metallurgical information existed about steel until 1860. Because of this lack of understanding, steel was not generally considered an alloy until the decades between 1930 and 1970 (primarily due to the work of scientists like William Chandler Roberts-Austen, Adolf Martens, and Edgar Bain), so "alloy steel" became the popular term for ternary and quaternary steel-alloys.
After Benjamin Huntsman developed his crucible steel in 1740, he began experimenting with the addition of elements like manganese (in the form of a high-manganese pig-iron called spiegeleisen), which helped remove impurities such as phosphorus and oxygen; a process adopted by Bessemer and still used in modern steels (albeit in concentrations low enough to still be considered carbon steel). Afterward, many people began experimenting with various alloys of steel without much success. However, in 1882, Robert Hadfield, being a pioneer in steel metallurgy, took an interest and produced a steel alloy containing around 12% manganese. Called mangalloy, it exhibited extreme hardness and toughness, becoming the first commercially viable alloy-steel. Afterward, he created silicon steel, launching the search for other possible alloys of steel. | Alloy | Wikipedia | 403 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
Robert Forester Mushet found that by adding tungsten to steel it could produce a very hard edge that would resist losing its hardness at high temperatures. "R. Mushet's special steel" (RMS) became the first high-speed steel. Mushet's steel was quickly replaced by tungsten carbide steel, developed by Taylor and White in 1900, in which they doubled the tungsten content and added small amounts of chromium and vanadium, producing a superior steel for use in lathes and machining tools. In 1903, the Wright brothers used a chromium-nickel steel to make the crankshaft for their airplane engine, while in 1908 Henry Ford began using vanadium steels for parts like crankshafts and valves in his Model T Ford, due to their higher strength and resistance to high temperatures. In 1912, the Krupp Ironworks in Germany developed a rust-resistant steel by adding 21% chromium and 7% nickel, producing the first stainless steel.
Others
Due to their high reactivity, most metals were not discovered until the 19th century. A method for extracting aluminium from bauxite was proposed by Humphry Davy in 1807, using an electric arc. Although his attempts were unsuccessful, by 1855 the first sales of pure aluminium reached the market. However, as extractive metallurgy was still in its infancy, most aluminium extraction-processes produced unintended alloys contaminated with other elements found in the ore; the most abundant of which was copper. These aluminium-copper alloys (at the time termed "aluminum bronze") preceded pure aluminium, offering greater strength and hardness over the soft, pure metal, and to a slight degree were found to be heat treatable. However, due to their softness and limited hardenability these alloys found little practical use, and were more of a novelty, until the Wright brothers used an aluminium alloy to construct the first airplane engine in 1903. During the time between 1865 and 1910, processes for extracting many other metals were discovered, such as chromium, vanadium, tungsten, iridium, cobalt, and molybdenum, and various alloys were developed. | Alloy | Wikipedia | 445 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
Prior to 1910, research mainly consisted of private individuals tinkering in their own laboratories. However, as the aircraft and automotive industries began growing, research into alloys became an industrial effort in the years following 1910, as new magnesium alloys were developed for pistons and wheels in cars, and pot metal for levers and knobs, and aluminium alloys developed for airframes and aircraft skins were put into use. The Doehler Die Casting Co. of Toledo, Ohio were known for the production of Brastil, a high tensile corrosion resistant bronze alloy. | Alloy | Wikipedia | 111 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
In Euclidean geometry, an angle or plane angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection. Angles are also formed by the intersection of two planes; these are called dihedral angles.
In any case, the resulting angle lies in a plane (spanned by the two rays or perpendicular to the line of plane-plane intersection).
The magnitude of an angle is called an angular measure or simply "angle". Two different angles may have the same measure, as in an isosceles triangle. "Angle" also denotes the angular sector, the infinite region of the plane bounded by the sides of an angle.
Angle of rotation is a measure conventionally defined as the ratio of a circular arc length to its radius, and may be a negative number. In the case of an ordinary angle, the arc is centered at the vertex and delimited by the sides. In the case of an angle of rotation, the arc is centered at the center of the rotation and delimited by any other point and its image after the rotation.
History and etymology
The word angle comes from the Latin word , meaning "corner". Cognate words include the Greek () meaning "crooked, curved" and the English word "ankle". Both are connected with the Proto-Indo-European root *ank-, meaning "to bend" or "bow".
Euclid defines a plane angle as the inclination to each other, in a plane, of two lines that meet each other and do not lie straight with respect to each other. According to the Neoplatonic metaphysician Proclus, an angle must be either a quality, a quantity, or a relationship. The first concept, angle as quality, was used by Eudemus of Rhodes, who regarded an angle as a deviation from a straight line; the second, angle as quantity, by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third: angle as a relationship. | Angle | Wikipedia | 452 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Identifying angles
In mathematical expressions, it is common to use Greek letters (α, β, γ, θ, φ, . . . ) as variables denoting the size of some angle (the symbol is typically not used for this purpose to avoid confusion with the constant denoted by that symbol). Lower case Roman letters (a, b, c, . . . ) are also used. In contexts where this is not confusing, an angle may be denoted by the upper case Roman letter denoting its vertex. See the figures in this article for examples.
The three defining points may also identify angles in geometric figures. For example, the angle with vertex A formed by the rays AB and AC (that is, the half-lines from point A through points B and C) is denoted or . Where there is no risk of confusion, the angle may sometimes be referred to by a single vertex alone (in this case, "angle A").
In other ways, an angle denoted as, say, might refer to any of four angles: the clockwise angle from B to C about A, the anticlockwise angle from B to C about A, the clockwise angle from C to B about A, or the anticlockwise angle from C to B about A, where the direction in which the angle is measured determines its sign (see ). However, in many geometrical situations, it is evident from the context that the positive angle less than or equal to 180 degrees is meant, and in these cases, no ambiguity arises. Otherwise, to avoid ambiguity, specific conventions may be adopted so that, for instance, always refers to the anticlockwise (positive) angle from B to C about A and the anticlockwise (positive) angle from C to B about A.
Types | Angle | Wikipedia | 362 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Individual angles
There is some common terminology for angles, whose measure is always non-negative (see ):
An angle equal to 0° or not turned is called a zero angle.
An angle smaller than a right angle (less than 90°) is called an acute angle ("acute" meaning "sharp").
An angle equal to turn (90° or radians) is called a right angle. Two lines that form a right angle are said to be normal, orthogonal, or perpendicular.
An angle larger than a right angle and smaller than a straight angle (between 90° and 180°) is called an obtuse angle ("obtuse" meaning "blunt").
An angle equal to turn (180° or radians) is called a straight angle.
An angle larger than a straight angle but less than 1 turn (between 180° and 360°) is called a reflex angle.
An angle equal to 1 turn (360° or 2 radians) is called a full angle, complete angle, round angle or perigon.
An angle that is not a multiple of a right angle is called an oblique angle.
The names, intervals, and measuring units are shown in the table below:
Vertical and angle pairs
When two straight lines intersect at a point, four angles are formed. Pairwise, these angles are named according to their location relative to each other.
A transversal is a line that intersects a pair of (often parallel) lines and is associated with exterior angles, interior angles, alternate exterior angles, alternate interior angles, corresponding angles, and consecutive interior angles.
Combining angle pairs
The angle addition postulate states that if B is in the interior of angle AOC, then
I.e., the measure of the angle AOC is the sum of the measure of angle AOB and the measure of angle BOC.
Three special angle pairs involve the summation of angles:
Polygon-related angles | Angle | Wikipedia | 394 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
An angle that is part of a simple polygon is called an interior angle if it lies on the inside of that simple polygon. A simple concave polygon has at least one interior angle, that is, a reflex angle. In Euclidean geometry, the measures of the interior angles of a triangle add up to radians, 180°, or turn; the measures of the interior angles of a simple convex quadrilateral add up to 2 radians, 360°, or 1 turn. In general, the measures of the interior angles of a simple convex polygon with n sides add up to (n − 2) radians, or (n − 2)180 degrees, (n − 2)2 right angles, or (n − 2) turn.
The supplement of an interior angle is called an exterior angle; that is, an interior angle and an exterior angle form a linear pair of angles. There are two exterior angles at each vertex of the polygon, each determined by extending one of the two sides of the polygon that meet at the vertex; these two angles are vertical and hence are equal. An exterior angle measures the amount of rotation one must make at a vertex to trace the polygon. If the corresponding interior angle is a reflex angle, the exterior angle should be considered negative. Even in a non-simple polygon, it may be possible to define the exterior angle. Still, one will have to pick an orientation of the plane (or surface) to decide the sign of the exterior angle measure. In Euclidean geometry, the sum of the exterior angles of a simple convex polygon, if only one of the two exterior angles is assumed at each vertex, will be one full turn (360°). The exterior angle here could be called a supplementary exterior angle. Exterior angles are commonly used in Logo Turtle programs when drawing regular polygons.
In a triangle, the bisectors of two exterior angles and the bisector of the other interior angle are concurrent (meet at a single point).
In a triangle, three intersection points, each of an external angle bisector with the opposite extended side, are collinear.
In a triangle, three intersection points, two between an interior angle bisector and the opposite side, and the third between the other exterior angle bisector and the opposite side extended are collinear. | Angle | Wikipedia | 480 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Some authors use the name exterior angle of a simple polygon to mean the explement exterior angle (not supplement!) of the interior angle. This conflicts with the above usage. | Angle | Wikipedia | 37 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Plane-related angles
The angle between two planes (such as two adjacent faces of a polyhedron) is called a dihedral angle. It may be defined as the acute angle between two lines normal to the planes.
The angle between a plane and an intersecting straight line is complementary to the angle between the intersecting line and the normal to the plane.
Measuring angles
The size of a geometric angle is usually characterized by the magnitude of the smallest rotation that maps one of the rays into the other. Angles of the same size are said to be equal congruent or equal in measure.
In some contexts, such as identifying a point on a circle or describing the orientation of an object in two dimensions relative to a reference orientation, angles that differ by an exact multiple of a full turn are effectively equivalent. In other contexts, such as identifying a point on a spiral curve or describing an object's cumulative rotation in two dimensions relative to a reference orientation, angles that differ by a non-zero multiple of a full turn are not equivalent.
To measure an angle θ, a circular arc centered at the vertex of the angle is drawn, e.g., with a pair of compasses. The ratio of the length s of the arc by the radius r of the circle is the number of radians in the angle:
Conventionally, in mathematics and the SI, the radian is treated as being equal to the dimensionless unit 1, thus being normally omitted.
The angle expressed by another angular unit may then be obtained by multiplying the angle by a suitable conversion constant of the form , where k is the measure of a complete turn expressed in the chosen unit (for example, for degrees or 400 grad for gradians):
The value of thus defined is independent of the size of the circle: if the length of the radius is changed, then the arc length changes in the same proportion, so the ratio s/r is unaltered.
Units | Angle | Wikipedia | 393 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Throughout history, angles have been measured in various units. These are known as angular units, with the most contemporary units being the degree ( ° ), the radian (rad), and the gradian (grad), though many others have been used throughout history. Most units of angular measurement are defined such that one turn (i.e., the angle subtended by the circumference of a circle at its centre) is equal to n units, for some whole number n. Two exceptions are the radian (and its decimal submultiples) and the diameter part.
In the International System of Quantities, an angle is defined as a dimensionless quantity, and in particular, the radian unit is dimensionless. This convention impacts how angles are treated in dimensional analysis.
The following table lists some units used to represent angles.
Dimensional analysis
Signed angles
It is frequently helpful to impose a convention that allows positive and negative angular values to represent orientations and/or rotations in opposite directions or "sense" relative to some reference.
In a two-dimensional Cartesian coordinate system, an angle is typically defined by its two sides, with its vertex at the origin. The initial side is on the positive x-axis, while the other side or terminal side is defined by the measure from the initial side in radians, degrees, or turns, with positive angles representing rotations toward the positive y-axis and negative angles representing rotations toward the negative y-axis. When Cartesian coordinates are represented by standard position, defined by the x-axis rightward and the y-axis upward, positive rotations are anticlockwise, and negative cycles are clockwise.
In many contexts, an angle of −θ is effectively equivalent to an angle of "one full turn minus θ". For example, an orientation represented as −45° is effectively equal to an orientation defined as 360° − 45° or 315°. Although the final position is the same, a physical rotation (movement) of −45° is not the same as a rotation of 315° (for example, the rotation of a person holding a broom resting on a dusty floor would leave visually different traces of swept regions on the floor). | Angle | Wikipedia | 454 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
In three-dimensional geometry, "clockwise" and "anticlockwise" have no absolute meaning, so the direction of positive and negative angles must be defined in terms of an orientation, which is typically determined by a normal vector passing through the angle's vertex and perpendicular to the plane in which the rays of the angle lie.
In navigation, bearings or azimuth are measured relative to north. By convention, viewed from above, bearing angles are positive clockwise, so a bearing of 45° corresponds to a north-east orientation. Negative bearings are not used in navigation, so a north-west orientation corresponds to a bearing of 315°.
Equivalent angles
Angles that have the same measure (i.e., the same magnitude) are said to be equal or congruent. An angle is defined by its measure and is not dependent upon the lengths of the sides of the angle (e.g., all right angles are equal in measure).
Two angles that share terminal sides, but differ in size by an integer multiple of a turn, are called coterminal angles.
The reference angle (sometimes called related angle) for any angle θ in standard position is the positive acute angle between the terminal side of θ and the x-axis (positive or negative). Procedurally, the magnitude of the reference angle for a given angle may determined by taking the angle's magnitude modulo turn, 180°, or radians, then stopping if the angle is acute, otherwise taking the supplementary angle, 180° minus the reduced magnitude. For example, an angle of 30 degrees is already a reference angle, and an angle of 150 degrees also has a reference angle of 30 degrees (180° − 150°). Angles of 210° and 510° correspond to a reference angle of 30 degrees as well (210° mod 180° = 30°, 510° mod 180° = 150° whose supplementary angle is 30°). | Angle | Wikipedia | 391 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Related quantities
For an angular unit, it is definitional that the angle addition postulate holds. Some quantities related to angles where the angle addition postulate does not hold include:
The slope or gradient is equal to the tangent of the angle; a gradient is often expressed as a percentage. For very small values (less than 5%), the slope of a line is approximately the measure in radians of its angle with the horizontal direction.
The spread between two lines is defined in rational geometry as the square of the sine of the angle between the lines. As the sine of an angle and the sine of its supplementary angle are the same, any angle of rotation that maps one of the lines into the other leads to the same value for the spread between the lines.
Although done rarely, one can report the direct results of trigonometric functions, such as the sine of the angle.
Angles between curves
The angle between a line and a curve (mixed angle) or between two intersecting curves (curvilinear angle) is defined to be the angle between the tangents at the point of intersection. Various names (now rarely, if ever, used) have been given to particular cases:—amphicyrtic (Gr. , on both sides, κυρτός, convex) or cissoidal (Gr. κισσός, ivy), biconvex; xystroidal or sistroidal (Gr. ξυστρίς, a tool for scraping), concavo-convex; amphicoelic (Gr. κοίλη, a hollow) or angulus lunularis, biconcave.
Bisecting and trisecting angles
The ancient Greek mathematicians knew how to bisect an angle (divide it into two angles of equal measure) using only a compass and straightedge but could only trisect certain angles. In 1837, Pierre Wantzel showed that this construction could not be performed for most angles.
Dot product and generalisations
In the Euclidean space, the angle θ between two Euclidean vectors u and v is related to their dot product and their lengths by the formula
This formula supplies an easy method to find the angle between two planes (or curved surfaces) from their normal vectors and between skew lines from their vector equations.
Inner product
To define angles in an abstract real inner product space, we replace the Euclidean dot product ( · ) by the inner product , i.e. | Angle | Wikipedia | 504 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
In a complex inner product space, the expression for the cosine above may give non-real values, so it is replaced with
or, more commonly, using the absolute value, with
The latter definition ignores the direction of the vectors. It thus describes the angle between one-dimensional subspaces and spanned by the vectors and correspondingly.
Angles between subspaces
The definition of the angle between one-dimensional subspaces and given by
in a Hilbert space can be extended to subspaces of finite dimensions. Given two subspaces , with , this leads to a definition of angles called canonical or principal angles between subspaces.
Angles in Riemannian geometry
In Riemannian geometry, the metric tensor is used to define the angle between two tangents. Where U and V are tangent vectors and gij are the components of the metric tensor G,
Hyperbolic angle
A hyperbolic angle is an argument of a hyperbolic function just as the circular angle is the argument of a circular function. The comparison can be visualized as the size of the openings of a hyperbolic sector and a circular sector since the areas of these sectors correspond to the angle magnitudes in each case. Unlike the circular angle, the hyperbolic angle is unbounded. When the circular and hyperbolic functions are viewed as infinite series in their angle argument, the circular ones are just alternating series forms of the hyperbolic functions. This comparison of the two series corresponding to functions of angles was described by Leonhard Euler in Introduction to the Analysis of the Infinite (1748).
Angles in geography and astronomy
In geography, the location of any point on the Earth can be identified using a geographic coordinate system. This system specifies the latitude and longitude of any location in terms of angles subtended at the center of the Earth, using the equator and (usually) the Greenwich meridian as references.
In astronomy, a given point on the celestial sphere (that is, the apparent position of an astronomical object) can be identified using any of several astronomical coordinate systems, where the references vary according to the particular system. Astronomers measure the angular separation of two stars by imagining two lines through the center of the Earth, each intersecting one of the stars. The angle between those lines and the angular separation between the two stars can be measured.
In both geography and astronomy, a sighting direction can be specified in terms of a vertical angle such as altitude /elevation with respect to the horizon as well as the azimuth with respect to north. | Angle | Wikipedia | 502 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Astronomers also measure objects' apparent size as an angular diameter. For example, the full moon has an angular diameter of approximately 0.5° when viewed from Earth. One could say, "The Moon's diameter subtends an angle of half a degree." The small-angle formula can convert such an angular measurement into a distance/size ratio.
Other astronomical approximations include:
0.5° is the approximate diameter of the Sun and of the Moon as viewed from Earth.
1° is the approximate width of the little finger at arm's length.
10° is the approximate width of a closed fist at arm's length.
20° is the approximate width of a handspan at arm's length.
These measurements depend on the individual subject, and the above should be treated as rough rule of thumb approximations only.
In astronomy, right ascension and declination are usually measured in angular units, expressed in terms of time, based on a 24-hour day. | Angle | Wikipedia | 199 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries.
Hearing is one of the most crucial means of survival in the animal world and speech is one of the most distinctive characteristics of human development and culture. Accordingly, the science of acoustics spreads across many facets of human society—music, medicine, architecture, industrial production, warfare and more. Likewise, animal species such as songbirds and frogs use sound and hearing as a key element of mating rituals or for marking territories. Art, craft, science and technology have provoked one another to advance the whole, as in many other fields of knowledge. Robert Bruce Lindsay's "Wheel of Acoustics" is a well-accepted overview of the various fields in acoustics.
History
Etymology
The word "acoustic" is derived from the Greek word ἀκουστικός (akoustikos), meaning "of or for hearing, ready to hear" and that from ἀκουστός (akoustos), "heard, audible", which in turn derives from the verb ἀκούω(akouo), "I hear".
The Latin synonym is "sonic", after which the term sonics used to be a synonym for acoustics and later a branch of acoustics. Frequencies above and below the audible range are called "ultrasonic" and "infrasonic", respectively.
Early research in acoustics | Acoustics | Wikipedia | 367 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
In the 6th century BC, the ancient Greek philosopher Pythagoras wanted to know why some combinations of musical sounds seemed more beautiful than others, and he found answers in terms of numerical ratios representing the harmonic overtone series on a string. He is reputed to have observed that when the lengths of vibrating strings are expressible as ratios of integers (e.g. 2 to 3, 3 to 4), the tones produced will be harmonious, and the smaller the integers the more harmonious the sounds. For example, a string of a certain length would sound particularly harmonious with a string of twice the length (other factors being equal). In modern parlance, if a string sounds the note C when plucked, a string twice as long will sound a C an octave lower. In one system of musical tuning, the tones in between are then given by 16:9 for D, 8:5 for E, 3:2 for F, 4:3 for G, 6:5 for A, and 16:15 for B, in ascending order.
Aristotle (384–322 BC) understood that sound consisted of compressions and rarefactions of air which "falls upon and strikes the air which is next to it...", a very good expression of the nature of wave motion. On Things Heard, generally ascribed to Strato of Lampsacus, states that the pitch is related to the frequency of vibrations of the air and to the speed of sound.
In about 20 BC, the Roman architect and engineer Vitruvius wrote a treatise on the acoustic properties of theaters including discussion of interference, echoes, and reverberation—the beginnings of architectural acoustics. In Book V of his (The Ten Books of Architecture) Vitruvius describes sound as a wave comparable to a water wave extended to three dimensions, which, when interrupted by obstructions, would flow back and break up following waves. He described the ascending seats in ancient theaters as designed to prevent this deterioration of sound and also recommended bronze vessels (echea) of appropriate sizes be placed in theaters to resonate with the fourth, fifth and so on, up to the double octave, in order to resonate with the more desirable, harmonious notes.
During the Islamic golden age, Abū Rayhān al-Bīrūnī (973–1048) is believed to have postulated that the speed of sound was much slower than the speed of light. | Acoustics | Wikipedia | 497 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
The physical understanding of acoustical processes advanced rapidly during and after the Scientific Revolution. Mainly Galileo Galilei (1564–1642) but also Marin Mersenne (1588–1648), independently, discovered the complete laws of vibrating strings (completing what Pythagoras and Pythagoreans had started 2000 years earlier). Galileo wrote "Waves are produced by the vibrations of a sonorous body, which spread through the air, bringing to the tympanum of the ear a stimulus which the mind interprets as sound", a remarkable statement that points to the beginnings of physiological and psychological acoustics. Experimental measurements of the speed of sound in air were carried out successfully between 1630 and 1680 by a number of investigators, prominently Mersenne. Meanwhile, Newton (1642–1727) derived the relationship for wave velocity in solids, a cornerstone of physical acoustics (Principia, 1687).
Age of Enlightenment and onward
Substantial progress in acoustics, resting on firmer mathematical and physical concepts, was made during the eighteenth century by Euler (1707–1783), Lagrange (1736–1813), and d'Alembert (1717–1783). During this era, continuum physics, or field theory, began to receive a definite mathematical structure. The wave equation emerged in a number of contexts, including the propagation of sound in air.
In the nineteenth century the major figures of mathematical acoustics were Helmholtz in Germany, who consolidated the field of physiological acoustics, and Lord Rayleigh in England, who combined the previous knowledge with his own copious contributions to the field in his monumental work The Theory of Sound (1877). Also in the 19th century, Wheatstone, Ohm, and Henry developed the analogy between electricity and acoustics.
The twentieth century saw a burgeoning of technological applications of the large body of scientific knowledge that was by then in place. The first such application was Sabine's groundbreaking work in architectural acoustics, and many others followed. Underwater acoustics was used for detecting submarines in the first World War. Sound recording and the telephone played important roles in a global transformation of society. Sound measurement and analysis reached new levels of accuracy and sophistication through the use of electronics and computing. The ultrasonic frequency range enabled wholly new kinds of application in medicine and industry. New kinds of transducers (generators and receivers of acoustic energy) were invented and put to use.
Definition | Acoustics | Wikipedia | 499 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
Acoustics is defined by ANSI/ASA S1.1-2013 as "(a) Science of sound, including its production, transmission, and effects, including biological and psychological effects. (b) Those qualities of a room that, together, determine its character with respect to auditory effects."
The study of acoustics revolves around the generation, propagation and reception of mechanical waves and vibrations.
The steps shown in the above diagram can be found in any acoustical event or process. There are many kinds of cause, both natural and volitional. There are many kinds of transduction process that convert energy from some other form into sonic energy, producing a sound wave. There is one fundamental equation that describes sound wave propagation, the acoustic wave equation, but the phenomena that emerge from it are varied and often complex. The wave carries energy throughout the propagating medium. Eventually this energy is transduced again into other forms, in ways that again may be natural and/or volitionally contrived. The final effect may be purely physical or it may reach far into the biological or volitional domains. The five basic steps are found equally well whether we are talking about an earthquake, a submarine using sonar to locate its foe, or a band playing in a rock concert.
The central stage in the acoustical process is wave propagation. This falls within the domain of physical acoustics. In fluids, sound propagates primarily as a pressure wave. In solids, mechanical waves can take many forms including longitudinal waves, transverse waves and surface waves.
Acoustics looks first at the pressure levels and frequencies in the sound wave and how the wave interacts with the environment. This interaction can be described as either a diffraction, interference or a reflection or a mix of the three. If several media are present, a refraction can also occur. Transduction processes are also of special importance to acoustics.
Fundamental concepts
Wave propagation: pressure levels
In fluids such as air and water, sound waves propagate as disturbances in the ambient pressure level. While this disturbance is usually small, it is still noticeable to the human ear. The smallest sound that a person can hear, known as the threshold of hearing, is nine orders of magnitude smaller than the ambient pressure. The loudness of these disturbances is related to the sound pressure level (SPL) which is measured on a logarithmic scale in decibels.
Wave propagation: frequency | Acoustics | Wikipedia | 492 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
Physicists and acoustic engineers tend to discuss sound pressure levels in terms of frequencies, partly because this is how our ears interpret sound. What we experience as "higher pitched" or "lower pitched" sounds are pressure vibrations having a higher or lower number of cycles per second. In a common technique of acoustic measurement, acoustic signals are sampled in time, and then presented in more meaningful forms such as octave bands or time frequency plots. Both of these popular methods are used to analyze sound and better understand the acoustic phenomenon.
The entire spectrum can be divided into three sections: audio, ultrasonic, and infrasonic. The audio range falls between 20 Hz and 20,000 Hz. This range is important because its frequencies can be detected by the human ear. This range has a number of applications, including speech communication and music. The ultrasonic range refers to the very high frequencies: 20,000 Hz and higher. This range has shorter wavelengths which allow better resolution in imaging technologies. Medical applications such as ultrasonography and elastography rely on the ultrasonic frequency range. On the other end of the spectrum, the lowest frequencies are known as the infrasonic range. These frequencies can be used to study geological phenomena such as earthquakes.
Analytic instruments such as the spectrum analyzer facilitate visualization and measurement of acoustic signals and their properties. The spectrogram produced by such an instrument is a graphical display of the time varying pressure level and frequency profiles which give a specific acoustic signal its defining character.
Transduction in acoustics
A transducer is a device for converting one form of energy into another. In an electroacoustic context, this means converting sound energy into electrical energy (or vice versa). Electroacoustic transducers include loudspeakers, microphones, particle velocity sensors, hydrophones and sonar projectors. These devices convert a sound wave to or from an electric signal. The most widely used transduction principles are electromagnetism, electrostatics and piezoelectricity. | Acoustics | Wikipedia | 406 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
The transducers in most common loudspeakers (e.g. woofers and tweeters), are electromagnetic devices that generate waves using a suspended diaphragm driven by an electromagnetic voice coil, sending off pressure waves. Electret microphones and condenser microphones employ electrostatics—as the sound wave strikes the microphone's diaphragm, it moves and induces a voltage change. The ultrasonic systems used in medical ultrasonography employ piezoelectric transducers. These are made from special ceramics in which mechanical vibrations and electrical fields are interlinked through a property of the material itself.
Acoustician
An acoustician is an expert in the science of sound.
Education
There are many types of acoustician, but they usually have a Bachelor's degree or higher qualification. Some possess a degree in acoustics, while others enter the discipline via studies in fields such as physics or engineering. Much work in acoustics requires a good grounding in Mathematics and science. Many acoustic scientists work in research and development. Some conduct basic research to advance our knowledge of the perception (e.g. hearing, psychoacoustics or neurophysiology) of speech, music and noise. Other acoustic scientists advance understanding of how sound is affected as it moves through environments, e.g. underwater acoustics, architectural acoustics or structural acoustics. Other areas of work are listed under subdisciplines below. Acoustic scientists work in government, university and private industry laboratories. Many go on to work in Acoustical Engineering. Some positions, such as Faculty (academic staff) require a Doctor of Philosophy.
Subdisciplines
Archaeoacoustics | Acoustics | Wikipedia | 346 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
Archaeoacoustics, also known as the archaeology of sound, is one of the only ways to experience the past with senses other than our eyes. Archaeoacoustics is studied by testing the acoustic properties of prehistoric sites, including caves. Iegor Rezkinoff, a sound archaeologist, studies the acoustic properties of caves through natural sounds like humming and whistling. Archaeological theories of acoustics are focused around ritualistic purposes as well as a way of echolocation in the caves. In archaeology, acoustic sounds and rituals directly correlate as specific sounds were meant to bring ritual participants closer to a spiritual awakening. Parallels can also be drawn between cave wall paintings and the acoustic properties of the cave; they are both dynamic. Because archaeoacoustics is a fairly new archaeological subject, acoustic sound is still being tested in these prehistoric sites today.
Aeroacoustics
Aeroacoustics is the study of noise generated by air movement, for instance via turbulence, and the movement of sound through the fluid air. This knowledge was applied in the 1920s and '30s to detect aircraft before radar was invented and is applied in acoustical engineering to study how to quieten aircraft. Aeroacoustics is important for understanding how wind musical instruments work.
Acoustic signal processing
Acoustic signal processing is the electronic manipulation of acoustic signals. Applications include: active noise control; design for hearing aids or cochlear implants; echo cancellation; music information retrieval, and perceptual coding (e.g. MP3 or Opus).
Architectural acoustics
Architectural acoustics (also known as building acoustics) involves the scientific understanding of how to achieve good sound within a building. It typically involves the study of speech intelligibility, speech privacy, music quality, and vibration reduction in the built environment. Commonly studied environments are hospitals, classrooms, dwellings, performance venues, recording and broadcasting studios. Focus considerations include room acoustics, airborne and impact transmission in building structures, airborne and structure-borne noise control, noise control of building systems and electroacoustic systems.
Bioacoustics
Bioacoustics is the scientific study of the hearing and calls of animal calls, as well as how animals are affected by the acoustic and sounds of their habitat.
Electroacoustics
This subdiscipline is concerned with the recording, manipulation and reproduction of audio using electronics. This might include products such as mobile phones, large scale public address systems or virtual reality systems in research laboratories.
Environmental noise and soundscapes | Acoustics | Wikipedia | 504 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
Environmental acoustics is the study of noise and vibrations, and their impact on structures, objects, humans, and animals.
The main aim of these studies is to reduce levels of environmental noise and vibration. Typical work and research within environmental acoustics concerns the development of models used in simulations, measurement techniques, noise mitigation strategies, and the development of standards and regulations. Research work now also has a focus on the positive use of sound in urban environments: soundscapes and tranquility.
Examples of noise and vibration sources include railways, road traffic, aircraft, industrial equipment and recreational activities.
Musical acoustics
Musical acoustics is the study of the physics of acoustic instruments; the audio signal processing used in electronic music; the computer analysis of music and composition, and the perception and cognitive neuroscience of music.
Psychoacoustics
Many studies have been conducted to identify the relationship between acoustics and cognition, or more commonly known as psychoacoustics, in which what one hears is a combination of perception and biological aspects. The information intercepted by the passage of sound waves through the ear is understood and interpreted through the brain, emphasizing the connection between the mind and acoustics. Psychological changes have been seen as brain waves slow down or speed up as a result of varying auditory stimulus which can in turn affect the way one thinks, feels, or even behaves. This correlation can be viewed in normal, everyday situations in which listening to an upbeat or uptempo song can cause one's foot to start tapping or a slower song can leave one feeling calm and serene. In a deeper biological look at the phenomenon of psychoacoustics, it was discovered that the central nervous system is activated by basic acoustical characteristics of music. By observing how the central nervous system, which includes the brain and spine, is influenced by acoustics, the pathway in which acoustic affects the mind, and essentially the body, is evident.
Speech
Acousticians study the production, processing and perception of speech. Speech recognition and Speech synthesis are two important areas of speech processing using computers. The subject also overlaps with the disciplines of physics, physiology, psychology, and linguistics.
Structural Vibration and Dynamics
Structural acoustics is the study of motions and interactions of mechanical systems with their environments and the methods of their measurement, analysis, and control. There are several sub-disciplines found within this regime:
Modal Analysis
Material characterization
Structural health monitoring
Acoustic Metamaterials
Friction Acoustics | Acoustics | Wikipedia | 488 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
Applications might include: ground vibrations from railways; vibration isolation to reduce vibration in operating theatres; studying how vibration can damage health (vibration white finger); vibration control to protect a building from earthquakes, or measuring how structure-borne sound moves through buildings.
Ultrasonics
Ultrasonics deals with sounds at frequencies too high to be heard by humans. Specialisms include medical ultrasonics (including medical ultrasonography), sonochemistry, ultrasonic testing, material characterisation and underwater acoustics (sonar).
Underwater acoustics
Underwater acoustics is the scientific study of natural and man-made sounds underwater. Applications include sonar to locate submarines, underwater communication by whales, climate change monitoring by measuring sea temperatures acoustically, sonic weapons, and marine bioacoustics.
Research
Professional societies
The Acoustical Society of America (ASA)
Australian Acoustical Society (AAS)
The European Acoustics Association (EAA)
Institute of Electrical and Electronics Engineers (IEEE)
Institute of Acoustics (IoA UK)
The Audio Engineering Society (AES)
American Society of Mechanical Engineers, Noise Control and Acoustics Division (ASME-NCAD)
International Commission for Acoustics (ICA)
American Institute of Aeronautics and Astronautics, Aeroacoustics (AIAA)
International Computer Music Association (ICMA)
Academic journals
Acoustics | An Open Access Journal from MDPI
Acoustics Today
Acta Acustica united with Acustica
Advances in Acoustics and Vibration
Applied Acoustics
Building Acoustics
IEEE Transacions on Ultrasonics, Ferroelectrics, and Frequency Control
Journal of the Acoustical Society of America (JASA)
Journal of the Acoustical Society of America, Express Letters (JASA-EL)
Journal of the Audio Engineering Society
Journal of Sound and Vibration (JSV)
Journal of Vibration and Acoustics American Society of Mechanical Engineers
MDPI Acoustics
Noise Control Engineering Journal
SAE International Journal of Vehicle Dynamics, Stability and NVH
Ultrasonics (journal)
Ultrasonics Sonochemistry
Wave Motion
Conferences
InterNoise
NoiseCon
Forum Acousticum
SAE Noise and Vibration Conference and Exhibition | Acoustics | Wikipedia | 425 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned with the way in which electrons are arranged around the nucleus and
the processes by which these arrangements change. This comprises ions, neutral atoms and, unless otherwise stated, it can be assumed that the term atom includes ions.
The term atomic physics can be associated with nuclear power and nuclear weapons, due to the synonymous use of atomic and nuclear in standard English. Physicists distinguish between atomic physics—which deals with the atom as a system consisting of a nucleus and electrons—and nuclear physics, which studies nuclear reactions and special properties of atomic nuclei.
As with many scientific fields, strict delineation can be highly contrived and atomic physics is often considered in the wider context of atomic, molecular, and optical physics. Physics research groups are usually so classified.
Isolated atoms
Atomic physics primarily considers atoms in isolation. Atomic models will consist of a single nucleus that may be surrounded by one or more bound electrons. It is not concerned with the formation of molecules (although much of the physics is identical), nor does it examine atoms in a solid state as condensed matter. It is concerned with processes such as ionization and excitation by photons or collisions with atomic particles.
While modelling atoms in isolation may not seem realistic, if one considers atoms in a gas or plasma then the time-scales for atom-atom interactions are huge in comparison to the atomic processes that are generally considered. This means that the individual atoms can be treated as if each were in isolation, as the vast majority of the time they are. By this consideration, atomic physics provides the underlying theory in plasma physics and atmospheric physics, even though both deal with very large numbers of atoms.
Electronic configuration
Electrons form notional shells around the nucleus. These are normally in a ground state but can be excited by the absorption of energy from light (photons), magnetic fields, or interaction with a colliding particle (typically ions or other electrons).
Electrons that populate a shell are said to be in a bound state. The energy necessary to remove an electron from its shell (taking it to infinity) is called the binding energy. Any quantity of energy absorbed by the electron in excess of this amount is converted to kinetic energy according to the conservation of energy. The atom is said to have undergone the process of ionization. | Atomic physics | Wikipedia | 498 | 1200 | https://en.wikipedia.org/wiki/Atomic%20physics | Physical sciences | Atomic physics | null |
If the electron absorbs a quantity of energy less than the binding energy, it will be transferred to an excited state. After a certain time, the electron in an excited state will "jump" (undergo a transition) to a lower state. In a neutral atom, the system will emit a photon of the difference in energy, since energy is conserved.
If an inner electron has absorbed more than the binding energy (so that the atom ionizes), then a more outer electron may undergo a transition to fill the inner orbital. In this case, a visible photon or a characteristic X-ray is emitted, or a phenomenon known as the Auger effect may take place, where the released energy is transferred to another bound electron, causing it to go into the continuum. The Auger effect allows one to multiply ionize an atom with a single photon.
There are rather strict selection rules as to the electronic configurations that can be reached by excitation by light — however, there are no such rules for excitation by collision processes.
Bohr Model of the Atom
The Bohr model, proposed by Niels Bohr in 1913, is a revolutionary theory describing the structure of the hydrogen atom. It introduced the idea of quantized orbits for electrons, combining classical and quantum physics.
Key Postulates of the Bohr Model
1.Electrons Move in Circular Orbits:
• Electrons revolve around the nucleus in fixed, circular paths called orbits or energy levels.
•These orbits are stable and do not radiate energy.
2.Quantization of Angular Momentum:
•The angular momentum of an electron is quantized and given by:
L = m_e v r = n\hbar, \quad n = 1, 2, 3, \dots
where:
• m_e : Mass of the electron.
• v : Velocity of the electron.
• r : Radius of the orbit.
• \hbar : Reduced Planck’s constant ( \hbar = \frac{h}{2\pi} ).
•n : Principal quantum number, representing the orbit.
3.Energy Levels:
•Each orbit has a specific energy. The total energy of an electron in the nth orbit is:
E_n = -\frac{13.6}{n^2} \ \text{eV},
where 13.6 \ \text{eV} is the ground-state energy of the hydrogen atom.
4.Emission or Absorption of Energy: | Atomic physics | Wikipedia | 502 | 1200 | https://en.wikipedia.org/wiki/Atomic%20physics | Physical sciences | Atomic physics | null |
•Electrons can transition between orbits by absorbing or emitting energy equal to the difference between the energy levels:
\Delta E = E_f - E_i = h\nu,
where:
•h : Planck’s constant.
• \nu : Frequency of emitted/absorbed radiation.
• E_f, E_i : Final and initial energy levels.
History and developments
One of the earliest steps towards atomic physics was the recognition that matter was composed
of atoms. It forms a part of the texts written in 6th century BC to 2nd century BC, such as those of Democritus or written by . This theory was later developed in the modern sense of the basic unit of a chemical element by the British chemist and physicist John Dalton in the 18th century. At this stage, it wasn't clear what atoms were, although they could be described and classified by their properties (in bulk). The invention of the periodic system of elements by Dmitri Mendeleev was another great step forward.
The true beginning of atomic physics is marked by the discovery of spectral lines and attempts to describe the phenomenon, most notably by Joseph von Fraunhofer. The study of these lines led to the Bohr atom model and to the birth of quantum mechanics. In seeking to explain atomic spectra, an entirely new mathematical model of matter was revealed. As far as atoms and their electron shells were concerned, not only did this yield a better overall description, i.e. the atomic orbital model, but it also provided a new theoretical basis for chemistry
(quantum chemistry) and spectroscopy.
Since the Second World War, both theoretical and experimental fields have advanced at a rapid pace. This can be attributed to progress in computing technology, which has allowed larger and more sophisticated models of atomic structure and associated collision processes. Similar technological advances in accelerators, detectors, magnetic field generation and lasers have greatly assisted experimental work.
Beyond the well-known phenomena wich can be describe with regular quantum mechanics chaotic processes can occour which need different descriptions.
Significant atomic physicists | Atomic physics | Wikipedia | 410 | 1200 | https://en.wikipedia.org/wiki/Atomic%20physics | Physical sciences | Atomic physics | null |
In quantum mechanics, an atomic orbital () is a function describing the location and wave-like behavior of an electron in an atom. This function describes an electron's charge distribution around the atom's nucleus, and can be used to calculate the probability of finding an electron in a specific region around the nucleus.
Each orbital in an atom is characterized by a set of values of three quantum numbers , , and , which respectively correspond to electron's energy, its orbital angular momentum, and its orbital angular momentum projected along a chosen axis (magnetic quantum number). The orbitals with a well-defined magnetic quantum number are generally complex-valued. Real-valued orbitals can be formed as linear combinations of and orbitals, and are often labeled using associated harmonic polynomials (e.g., xy, ) which describe their angular structure.
An orbital can be occupied by a maximum of two electrons, each with its own projection of spin . The simple names s orbital, p orbital, d orbital, and f orbital refer to orbitals with angular momentum quantum number and respectively. These names, together with their n values, are used to describe electron configurations of atoms. They are derived from description by early spectroscopists of certain series of alkali metal spectroscopic lines as sharp, principal, diffuse, and fundamental. Orbitals for continue alphabetically (g, h, i, k, ...), omitting j because some languages do not distinguish between letters "i" and "j".
Atomic orbitals are basic building blocks of the atomic orbital model (or electron cloud or wave mechanics model), a modern framework for visualizing submicroscopic behavior of electrons in matter. In this model, the electron cloud of an atom may be seen as being built up (in approximation) in an electron configuration that is a product of simpler hydrogen-like atomic orbitals. The repeating periodicity of blocks of 2, 6, 10, and 14 elements within sections of periodic table arises naturally from total number of electrons that occupy a complete set of s, p, d, and f orbitals, respectively, though for higher values of quantum number , particularly when the atom bears a positive charge, energies of certain sub-shells become very similar and so, order in which they are said to be populated by electrons (e.g., Cr = [Ar]4s13d5 and Cr2+ = [Ar]3d4) can be rationalized only somewhat arbitrarily. | Atomic orbital | Wikipedia | 509 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Electron properties
With the development of quantum mechanics and experimental findings (such as the two slit diffraction of electrons), it was found that the electrons orbiting a nucleus could not be fully described as particles, but needed to be explained by wave–particle duality. In this sense, electrons have the following properties:
Wave-like properties:
Electrons do not orbit a nucleus in the manner of a planet orbiting a star, but instead exist as standing waves. Thus the lowest possible energy an electron can take is similar to the fundamental frequency of a wave on a string. Higher energy states are similar to harmonics of that fundamental frequency.
The electrons are never in a single point location, though the probability of interacting with the electron at a single point can be found from the electron's wave function. The electron's charge acts like it is smeared out in space in a continuous distribution, proportional at any point to the squared magnitude of the electron's wave function.
Particle-like properties:
The number of electrons orbiting a nucleus can be only an integer.
Electrons jump between orbitals like particles. For example, if one photon strikes the electrons, only one electron changes state as a result.
Electrons retain particle-like properties such as: each wave state has the same electric charge as its electron particle. Each wave state has a single discrete spin (spin up or spin down) depending on its superposition.
Thus, electrons cannot be described simply as solid particles. An analogy might be that of a large and often oddly shaped "atmosphere" (the electron), distributed around a relatively tiny planet (the nucleus). Atomic orbitals exactly describe the shape of this "atmosphere" only when one electron is present. When more electrons are added, the additional electrons tend to more evenly fill in a volume of space around the nucleus so that the resulting collection ("electron cloud") tends toward a generally spherical zone of probability describing the electron's location, because of the uncertainty principle. | Atomic orbital | Wikipedia | 396 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
One should remember that these orbital 'states', as described here, are merely eigenstates of an electron in its orbit. An actual electron exists in a superposition of states, which is like a weighted average, but with complex number weights. So, for instance, an electron could be in a pure eigenstate (2, 1, 0), or a mixed state (2, 1, 0) + (2, 1, 1), or even the mixed state (2, 1, 0) + (2, 1, 1). For each eigenstate, a property has an eigenvalue. So, for the three states just mentioned, the value of is 2, and the value of is 1. For the second and third states, the value for is a superposition of 0 and 1. As a superposition of states, it is ambiguous—either exactly 0 or exactly 1—not an intermediate or average value like the fraction . A superposition of eigenstates (2, 1, 1) and (3, 2, 1) would have an ambiguous and , but would definitely be 1. Eigenstates make it easier to deal with the math. You can choose a different basis of eigenstates by superimposing eigenstates from any other basis (see Real orbitals below).
Formal quantum mechanical definition
Atomic orbitals may be defined more precisely in formal quantum mechanical language. They are approximate solutions to the Schrödinger equation for the electrons bound to the atom by the electric field of the atom's nucleus. Specifically, in quantum mechanics, the state of an atom, i.e., an eigenstate of the atomic Hamiltonian, is approximated by an expansion (see configuration interaction expansion and basis set) into linear combinations of anti-symmetrized products (Slater determinants) of one-electron functions. The spatial components of these one-electron functions are called atomic orbitals. (When one considers also their spin component, one speaks of atomic spin orbitals.) A state is actually a function of the coordinates of all the electrons, so that their motion is correlated, but this is often approximated by this independent-particle model of products of single electron wave functions. (The London dispersion force, for example, depends on the correlations of the motion of the electrons.) | Atomic orbital | Wikipedia | 492 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
In atomic physics, the atomic spectral lines correspond to transitions (quantum leaps) between quantum states of an atom. These states are labeled by a set of quantum numbers summarized in the term symbol and usually associated with particular electron configurations, i.e., by occupation schemes of atomic orbitals (for example, 1s2 2s2 2p6 for the ground state of neon-term symbol: 1S0).
This notation means that the corresponding Slater determinants have a clear higher weight in the configuration interaction expansion. The atomic orbital concept is therefore a key concept for visualizing the excitation process associated with a given transition. For example, one can say for a given transition that it corresponds to the excitation of an electron from an occupied orbital to a given unoccupied orbital. Nevertheless, one has to keep in mind that electrons are fermions ruled by the Pauli exclusion principle and cannot be distinguished from each other. Moreover, it sometimes happens that the configuration interaction expansion converges very slowly and that one cannot speak about simple one-determinant wave function at all. This is the case when electron correlation is large.
Fundamentally, an atomic orbital is a one-electron wave function, even though many electrons are not in one-electron atoms, and so the one-electron view is an approximation. When thinking about orbitals, we are often given an orbital visualization heavily influenced by the Hartree–Fock approximation, which is one way to reduce the complexities of molecular orbital theory.
Types of orbital | Atomic orbital | Wikipedia | 311 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Atomic orbitals can be the hydrogen-like "orbitals" which are exact solutions to the Schrödinger equation for a hydrogen-like "atom" (i.e., atom with one electron). Alternatively, atomic orbitals refer to functions that depend on the coordinates of one electron (i.e., orbitals) but are used as starting points for approximating wave functions that depend on the simultaneous coordinates of all the electrons in an atom or molecule. The coordinate systems chosen for orbitals are usually spherical coordinates in atoms and Cartesian in polyatomic molecules. The advantage of spherical coordinates here is that an orbital wave function is a product of three factors each dependent on a single coordinate: . The angular factors of atomic orbitals generate s, p, d, etc. functions as real combinations of spherical harmonics (where and are quantum numbers). There are typically three mathematical forms for the radial functions which can be chosen as a starting point for the calculation of the properties of atoms and molecules with many electrons:
The hydrogen-like orbitals are derived from the exact solutions of the Schrödinger equation for one electron and a nucleus, for a hydrogen-like atom. The part of the function that depends on distance r from the nucleus has radial nodes and decays as .
The Slater-type orbital (STO) is a form without radial nodes but decays from the nucleus as does a hydrogen-like orbital.
The form of the Gaussian type orbital (Gaussians) has no radial nodes and decays as .
Although hydrogen-like orbitals are still used as pedagogical tools, the advent of computers has made STOs preferable for atoms and diatomic molecules since combinations of STOs can replace the nodes in hydrogen-like orbitals. Gaussians are typically used in molecules with three or more atoms. Although not as accurate by themselves as STOs, combinations of many Gaussians can attain the accuracy of hydrogen-like orbitals.
History | Atomic orbital | Wikipedia | 405 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
The term orbital was introduced by Robert S. Mulliken in 1932 as short for one-electron orbital wave function. Niels Bohr explained around 1913 that electrons might revolve around a compact nucleus with definite angular momentum. Bohr's model was an improvement on the 1911 explanations of Ernest Rutherford, that of the electron moving around a nucleus. Japanese physicist Hantaro Nagaoka published an orbit-based hypothesis for electron behavior as early as 1904. These theories were each built upon new observations starting with simple understanding and becoming more correct and complex. Explaining the behavior of these electron "orbits" was one of the driving forces behind the development of quantum mechanics.
Early models
With J. J. Thomson's discovery of the electron in 1897, it became clear that atoms were not the smallest building blocks of nature, but were rather composite particles. The newly discovered structure within atoms tempted many to imagine how the atom's constituent parts might interact with each other. Thomson theorized that multiple electrons revolve in orbit-like rings within a positively charged jelly-like substance, and between the electron's discovery and 1909, this "plum pudding model" was the most widely accepted explanation of atomic structure.
Shortly after Thomson's discovery, Hantaro Nagaoka predicted a different model for electronic structure. Unlike the plum pudding model, the positive charge in Nagaoka's "Saturnian Model" was concentrated into a central core, pulling the electrons into circular orbits reminiscent of Saturn's rings. Few people took notice of Nagaoka's work at the time, and Nagaoka himself recognized a fundamental defect in the theory even at its conception, namely that a classical charged object cannot sustain orbital motion because it is accelerating and therefore loses energy due to electromagnetic radiation. Nevertheless, the Saturnian model turned out to have more in common with modern theory than any of its contemporaries. | Atomic orbital | Wikipedia | 374 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Bohr atom
In 1909, Ernest Rutherford discovered that the bulk of the atomic mass was tightly condensed into a nucleus, which was also found to be positively charged. It became clear from his analysis in 1911 that the plum pudding model could not explain atomic structure. In 1913, Rutherford's post-doctoral student, Niels Bohr, proposed a new model of the atom, wherein electrons orbited the nucleus with classical periods, but were permitted to have only discrete values of angular momentum, quantized in units ħ. This constraint automatically allowed only certain electron energies. The Bohr model of the atom fixed the problem of energy loss from radiation from a ground state (by declaring that there was no state below this), and more importantly explained the origin of spectral lines.
After Bohr's use of Einstein's explanation of the photoelectric effect to relate energy levels in atoms with the wavelength of emitted light, the connection between the structure of electrons in atoms and the emission and absorption spectra of atoms became an increasingly useful tool in the understanding of electrons in atoms. The most prominent feature of emission and absorption spectra (known experimentally since the middle of the 19th century), was that these atomic spectra contained discrete lines. The significance of the Bohr model was that it related the lines in emission and absorption spectra to the energy differences between the orbits that electrons could take around an atom. This was, however, not achieved by Bohr through giving the electrons some kind of wave-like properties, since the idea that electrons could behave as matter waves was not suggested until eleven years later. Still, the Bohr model's use of quantized angular momenta and therefore quantized energy levels was a significant step toward the understanding of electrons in atoms, and also a significant step towards the development of quantum mechanics in suggesting that quantized restraints must account for all discontinuous energy levels and spectra in atoms. | Atomic orbital | Wikipedia | 382 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
With de Broglie's suggestion of the existence of electron matter waves in 1924, and for a short time before the full 1926 Schrödinger equation treatment of hydrogen-like atoms, a Bohr electron "wavelength" could be seen to be a function of its momentum; so a Bohr orbiting electron was seen to orbit in a circle at a multiple of its half-wavelength. The Bohr model for a short time could be seen as a classical model with an additional constraint provided by the 'wavelength' argument. However, this period was immediately superseded by the full three-dimensional wave mechanics of 1926. In our current understanding of physics, the Bohr model is called a semi-classical model because of its quantization of angular momentum, not primarily because of its relationship with electron wavelength, which appeared in hindsight a dozen years after the Bohr model was proposed.
The Bohr model was able to explain the emission and absorption spectra of hydrogen. The energies of electrons in the n = 1, 2, 3, etc. states in the Bohr model match those of current physics. However, this did not explain similarities between different atoms, as expressed by the periodic table, such as the fact that helium (two electrons), neon (10 electrons), and argon (18 electrons) exhibit similar chemical inertness. Modern quantum mechanics explains this in terms of electron shells and subshells which can each hold a number of electrons determined by the Pauli exclusion principle. Thus the n = 1 state can hold one or two electrons, while the n = 2 state can hold up to eight electrons in 2s and 2p subshells. In helium, all n = 1 states are fully occupied; the same is true for n = 1 and n = 2 in neon. In argon, the 3s and 3p subshells are similarly fully occupied by eight electrons; quantum mechanics also allows a 3d subshell but this is at higher energy than the 3s and 3p in argon (contrary to the situation for hydrogen) and remains empty. | Atomic orbital | Wikipedia | 424 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Modern conceptions and connections to the Heisenberg uncertainty principle
Immediately after Heisenberg discovered his uncertainty principle, Bohr noted that the existence of any sort of wave packet implies uncertainty in the wave frequency and wavelength, since a spread of frequencies is needed to create the packet itself. In quantum mechanics, where all particle momenta are associated with waves, it is the formation of such a wave packet which localizes the wave, and thus the particle, in space. In states where a quantum mechanical particle is bound, it must be localized as a wave packet, and the existence of the packet and its minimum size implies a spread and minimal value in particle wavelength, and thus also momentum and energy. In quantum mechanics, as a particle is localized to a smaller region in space, the associated compressed wave packet requires a larger and larger range of momenta, and thus larger kinetic energy. Thus the binding energy to contain or trap a particle in a smaller region of space increases without bound as the region of space grows smaller. Particles cannot be restricted to a geometric point in space, since this would require infinite particle momentum.
In chemistry, Erwin Schrödinger, Linus Pauling, Mulliken and others noted that the consequence of Heisenberg's relation was that the electron, as a wave packet, could not be considered to have an exact location in its orbital. Max Born suggested that the electron's position needed to be described by a probability distribution which was connected with finding the electron at some point in the wave-function which described its associated wave packet. The new quantum mechanics did not give exact results, but only the probabilities for the occurrence of a variety of possible such results. Heisenberg held that the path of a moving particle has no meaning if we cannot observe it, as we cannot with electrons in an atom.
In the quantum picture of Heisenberg, Schrödinger and others, the Bohr atom number n for each orbital became known as an n-sphere in a three-dimensional atom and was pictured as the most probable energy of the probability cloud of the electron's wave packet which surrounded the atom.
Orbital names
Orbital notation and subshells
Orbitals have been given names, which are usually given in the form:
where X is the energy level corresponding to the principal quantum number ; type is a lower-case letter denoting the shape or subshell of the orbital, corresponding to the angular momentum quantum number . | Atomic orbital | Wikipedia | 496 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
For example, the orbital 1s (pronounced as the individual numbers and letters: "'one' 'ess'") is the lowest energy level () and has an angular quantum number of , denoted as s. Orbitals with are denoted as p, d and f respectively.
The set of orbitals for a given n and is called a subshell, denoted
.
The superscript y shows the number of electrons in the subshell. For example, the notation 2p4 indicates that the 2p subshell of an atom contains 4 electrons. This subshell has 3 orbitals, each with n = 2 and = 1.
X-ray notation
There is also another, less common system still used in X-ray science known as X-ray notation, which is a continuation of the notations used before orbital theory was well understood. In this system, the principal quantum number is given a letter associated with it. For , the letters associated with those numbers are K, L, M, N, O, ... respectively.
Hydrogen-like orbitals
The simplest atomic orbitals are those that are calculated for systems with a single electron, such as the hydrogen atom. An atom of any other element ionized down to a single electron (He+, Li2+, etc.) is very similar to hydrogen, and the orbitals take the same form. In the Schrödinger equation for this system of one negative and one positive particle, the atomic orbitals are the eigenstates of the Hamiltonian operator for the energy. They can be obtained analytically, meaning that the resulting orbitals are products of a polynomial series, and exponential and trigonometric functions. (see hydrogen atom).
For atoms with two or more electrons, the governing equations can be solved only with the use of methods of iterative approximation. Orbitals of multi-electron atoms are qualitatively similar to those of hydrogen, and in the simplest models, they are taken to have the same form. For more rigorous and precise analysis, numerical approximations must be used.
A given (hydrogen-like) atomic orbital is identified by unique values of three quantum numbers: , , and . The rules restricting the values of the quantum numbers, and their energies (see below), explain the electron configuration of the atoms and the periodic table. | Atomic orbital | Wikipedia | 478 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
The stationary states (quantum states) of a hydrogen-like atom are its atomic orbitals. However, in general, an electron's behavior is not fully described by a single orbital. Electron states are best represented by time-depending "mixtures" (linear combinations) of multiple orbitals. See Linear combination of atomic orbitals molecular orbital method.
The quantum number first appeared in the Bohr model where it determines the radius of each circular electron orbit. In modern quantum mechanics however, determines the mean distance of the electron from the nucleus; all electrons with the same value of n lie at the same average distance. For this reason, orbitals with the same value of n are said to comprise a "shell". Orbitals with the same value of n and also the same value of are even more closely related, and are said to comprise a "subshell".
Quantum numbers
Because of the quantum mechanical nature of the electrons around a nucleus, atomic orbitals can be uniquely defined by a set of integers known as quantum numbers. These quantum numbers occur only in certain combinations of values, and their physical interpretation changes depending on whether real or complex versions of the atomic orbitals are employed.
Complex orbitals
In physics, the most common orbital descriptions are based on the solutions to the hydrogen atom, where orbitals are given by the product between a radial function and a pure spherical harmonic. The quantum numbers, together with the rules governing their possible values, are as follows:
The principal quantum number describes the energy of the electron and is always a positive integer. In fact, it can be any positive integer, but for reasons discussed below, large numbers are seldom encountered. Each atom has, in general, many orbitals associated with each value of n; these orbitals together are sometimes called electron shells.
The azimuthal quantum number describes the orbital angular momentum of each electron and is a non-negative integer. Within a shell where is some integer , ranges across all (integer) values satisfying the relation . For instance, the shell has only orbitals with , and the shell has only orbitals with , and . The set of orbitals associated with a particular value of are sometimes collectively called a subshell.
The magnetic quantum number, , describes the projection of the orbital angular momentum along a chosen axis. It determines the magnitude of the current circulating around that axis and the orbital contribution to the magnetic moment of an electron via the Ampèrian loop model. Within a subshell , obtains the integer values in the range . | Atomic orbital | Wikipedia | 509 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
The above results may be summarized in the following table. Each cell represents a subshell, and lists the values of available in that subshell. Empty cells represent subshells that do not exist.
Subshells are usually identified by their - and -values. is represented by its numerical value, but is represented by a letter as follows: 0 is represented by 's', 1 by 'p', 2 by 'd', 3 by 'f', and 4 by 'g'. For instance, one may speak of the subshell with and as a '2s subshell'.
Each electron also has angular momentum in the form of quantum mechanical spin given by spin s = . Its projection along a specified axis is given by the spin magnetic quantum number, ms, which can be + or −. These values are also called "spin up" or "spin down" respectively.
The Pauli exclusion principle states that no two electrons in an atom can have the same values of all four quantum numbers. If there are two electrons in an orbital with given values for three quantum numbers, (, , ), these two electrons must differ in their spin projection ms.
The above conventions imply a preferred axis (for example, the z direction in Cartesian coordinates), and they also imply a preferred direction along this preferred axis. Otherwise there would be no sense in distinguishing from . As such, the model is most useful when applied to physical systems that share these symmetries. The Stern–Gerlach experimentwhere an atom is exposed to a magnetic fieldprovides one such example.
Real orbitals
Instead of the complex orbitals described above, it is common, especially in the chemistry literature, to use real atomic orbitals. These real orbitals arise from simple linear combinations of complex orbitals. Using the Condon–Shortley phase convention, real orbitals are related to complex orbitals in the same way that the real spherical harmonics are related to complex spherical harmonics. Letting denote a complex orbital with quantum numbers , , and , the real orbitals may be defined by
If , with the radial part of the orbital, this definition is equivalent to where is the real spherical harmonic related to either the real or imaginary part of the complex spherical harmonic . | Atomic orbital | Wikipedia | 466 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Real spherical harmonics are physically relevant when an atom is embedded in a crystalline solid, in which case there are multiple preferred symmetry axes but no single preferred direction. Real atomic orbitals are also more frequently encountered in introductory chemistry textbooks and shown in common orbital visualizations. In real hydrogen-like orbitals, quantum numbers and have the same interpretation and significance as their complex counterparts, but is no longer a good quantum number (but its absolute value is).
Some real orbitals are given specific names beyond the simple designation. Orbitals with quantum number are called orbitals. With this one can already assign names to complex orbitals such as ; the first symbol is the quantum number, the second character is the symbol for that particular quantum number and the subscript is the quantum number.
As an example of how the full orbital names are generated for real orbitals, one may calculate . From the table of spherical harmonics, with . Then
Likewise . As a more complicated example:
In all these cases we generate a Cartesian label for the orbital by examining, and abbreviating, the polynomial in appearing in the numerator. We ignore any terms in the polynomial except for the term with the highest exponent in .
We then use the abbreviated polynomial as a subscript label for the atomic state, using the same nomenclature as above to indicate the and quantum numbers.
The expression above all use the Condon–Shortley phase convention which is favored by quantum physicists. Other conventions exist for the phase of the spherical harmonics. Under these different conventions the and orbitals may appear, for example, as the sum and difference of and , contrary to what is shown above.
Below is a list of these Cartesian polynomial names for the atomic orbitals. There does not seem to be reference in the literature as to how to abbreviate the long Cartesian spherical harmonic polynomials for so there does not seem be consensus on the naming of orbitals or higher according to this nomenclature.
Shapes of orbitals | Atomic orbital | Wikipedia | 402 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Simple pictures showing orbital shapes are intended to describe the angular forms of regions in space where the electrons occupying the orbital are likely to be found. The diagrams cannot show the entire region where an electron can be found, since according to quantum mechanics there is a non-zero probability of finding the electron (almost) anywhere in space. Instead the diagrams are approximate representations of boundary or contour surfaces where the probability density has a constant value, chosen so that there is a certain probability (for example 90%) of finding the electron within the contour. Although as the square of an absolute value is everywhere non-negative, the sign of the wave function is often indicated in each subregion of the orbital picture.
Sometimes the function is graphed to show its phases, rather than which shows probability density but has no phase (which is lost when taking absolute value, since is a complex number). orbital graphs tend to have less spherical, thinner lobes than graphs, but have the same number of lobes in the same places, and otherwise are recognizable. This article, to show wave function phase, shows mostly graphs.
The lobes can be seen as standing wave interference patterns between the two counter-rotating, ring-resonant traveling wave and modes; the projection of the orbital onto the xy plane has a resonant wavelength around the circumference. Although rarely shown, the traveling wave solutions can be seen as rotating banded tori; the bands represent phase information. For each there are two standing wave solutions and . If , the orbital is vertical, counter rotating information is unknown, and the orbital is z-axis symmetric. If there are no counter rotating modes. There are only radial modes and the shape is spherically symmetric.
Nodal planes and nodal spheres are surfaces on which the probability density vanishes. The number of nodal surfaces is controlled by the quantum numbers and . An orbital with azimuthal quantum number has radial nodal planes passing through the origin. For example, the s orbitals () are spherically symmetric and have no nodal planes, whereas the p orbitals () have a single nodal plane between the lobes. The number of nodal spheres equals , consistent with the restriction on the quantum numbers. The principal quantum number controls the total number of nodal surfaces which is . Loosely speaking, is energy, is analogous to eccentricity, and is orientation. | Atomic orbital | Wikipedia | 481 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
In general, determines size and energy of the orbital for a given nucleus; as increases, the size of the orbital increases. The higher nuclear charge of heavier elements causes their orbitals to contract by comparison to lighter ones, so that the size of the atom remains very roughly constant, even as the number of electrons increases.
Also in general terms, determines an orbital's shape, and its orientation. However, since some orbitals are described by equations in complex numbers, the shape sometimes depends on also. Together, the whole set of orbitals for a given and fill space as symmetrically as possible, though with increasingly complex sets of lobes and nodes.
The single s orbitals () are shaped like spheres. For it is roughly a solid ball (densest at center and fades outward exponentially), but for , each single s orbital is made of spherically symmetric surfaces which are nested shells (i.e., the "wave-structure" is radial, following a sinusoidal radial component as well). See illustration of a cross-section of these nested shells, at right. The s orbitals for all numbers are the only orbitals with an anti-node (a region of high wave function density) at the center of the nucleus. All other orbitals (p, d, f, etc.) have angular momentum, and thus avoid the nucleus (having a wave node at the nucleus). Recently, there has been an effort to experimentally image the 1s and 2p orbitals in a SrTiO3 crystal using scanning transmission electron microscopy with energy dispersive x-ray spectroscopy. Because the imaging was conducted using an electron beam, Coulombic beam-orbital interaction that is often termed as the impact parameter effect is included in the outcome (see the figure at right).
The shapes of p, d and f orbitals are described verbally here and shown graphically in the Orbitals table below. The three p orbitals for have the form of two ellipsoids with a point of tangency at the nucleus (the two-lobed shape is sometimes referred to as a "dumbbell"—there are two lobes pointing in opposite directions from each other). The three p orbitals in each shell are oriented at right angles to each other, as determined by their respective linear combination of values of . The overall result is a lobe pointing along each direction of the primary axes. | Atomic orbital | Wikipedia | 494 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Four of the five d orbitals for look similar, each with four pear-shaped lobes, each lobe tangent at right angles to two others, and the centers of all four lying in one plane. Three of these planes are the xy-, xz-, and yz-planes—the lobes are between the pairs of primary axes—and the fourth has the center along the x and y axes themselves. The fifth and final d orbital consists of three regions of high probability density: a torus in between two pear-shaped regions placed symmetrically on its z axis. The overall total of 18 directional lobes point in every primary axis direction and between every pair.
There are seven f orbitals, each with shapes more complex than those of the d orbitals.
Additionally, as is the case with the s orbitals, individual p, d, f and g orbitals with values higher than the lowest possible value, exhibit an additional radial node structure which is reminiscent of harmonic waves of the same type, as compared with the lowest (or fundamental) mode of the wave. As with s orbitals, this phenomenon provides p, d, f, and g orbitals at the next higher possible value of (for example, 3p orbitals vs. the fundamental 2p), an additional node in each lobe. Still higher values of further increase the number of radial nodes, for each type of orbital.
The shapes of atomic orbitals in one-electron atom are related to 3-dimensional spherical harmonics. These shapes are not unique, and any linear combination is valid, like a transformation to cubic harmonics, in fact it is possible to generate sets where all the d's are the same shape, just like the and are the same shape.
Although individual orbitals are most often shown independent of each other, the orbitals coexist around the nucleus at the same time. Also, in 1927, Albrecht Unsöld proved that if one sums the electron density of all orbitals of a particular azimuthal quantum number of the same shell (e.g., all three 2p orbitals, or all five 3d orbitals) where each orbital is occupied by an electron or each is occupied by an electron pair, then all angular dependence disappears; that is, the resulting total density of all the atomic orbitals in that subshell (those with the same ) is spherical. This is known as Unsöld's theorem. | Atomic orbital | Wikipedia | 496 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Orbitals table
This table shows the real hydrogen-like wave functions for all atomic orbitals up to 7s, and therefore covers the occupied orbitals in the ground state of all elements in the periodic table up to radium and some beyond. "ψ" graphs are shown with − and + wave function phases shown in two different colors (arbitrarily red and blue). The orbital is the same as the orbital, but the and are formed by taking linear combinations of the and orbitals (which is why they are listed under the label). Also, the and are not the same shape as the , since they are pure spherical harmonics.
* No elements with 6f, 7d or 7f electrons have been discovered yet.
† Elements with 7p electrons have been discovered, but their electronic configurations are only predicted – save the exceptional Lr, which fills 7p1 instead of 6d1.
‡ For the elements whose highest occupied orbital is a 6d orbital, only some electronic configurations have been confirmed. (Mt, Ds, Rg and Cn are still missing).
These are the real-valued orbitals commonly used in chemistry. Only the orbitals where are eigenstates of the orbital angular momentum operator, . The columns with are combinations of two eigenstates. See comparison in the following picture: | Atomic orbital | Wikipedia | 271 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Qualitative understanding of shapes
The shapes of atomic orbitals can be qualitatively understood by considering the analogous case of standing waves on a circular drum. To see the analogy, the mean vibrational displacement of each bit of drum membrane from the equilibrium point over many cycles (a measure of average drum membrane velocity and momentum at that point) must be considered relative to that point's distance from the center of the drum head. If this displacement is taken as being analogous to the probability of finding an electron at a given distance from the nucleus, then it will be seen that the many modes of the vibrating disk form patterns that trace the various shapes of atomic orbitals. The basic reason for this correspondence lies in the fact that the distribution of kinetic energy and momentum in a matter-wave is predictive of where the particle associated with the wave will be. That is, the probability of finding an electron at a given place is also a function of the electron's average momentum at that point, since high electron momentum at a given position tends to "localize" the electron in that position, via the properties of electron wave-packets (see the Heisenberg uncertainty principle for details of the mechanism).
This relationship means that certain key features can be observed in both drum membrane modes and atomic orbitals. For example, in all of the modes analogous to s orbitals (the top row in the animated illustration below), it can be seen that the very center of the drum membrane vibrates most strongly, corresponding to the antinode in all s orbitals in an atom. This antinode means the electron is most likely to be at the physical position of the nucleus (which it passes straight through without scattering or striking it), since it is moving (on average) most rapidly at that point, giving it maximal momentum.
A mental "planetary orbit" picture closest to the behavior of electrons in s orbitals, all of which have no angular momentum, might perhaps be that of a Keplerian orbit with the orbital eccentricity of 1 but a finite major axis, not physically possible (because particles were to collide), but can be imagined as a limit of orbits with equal major axes but increasing eccentricity.
Below, a number of drum membrane vibration modes and the respective wave functions of the hydrogen atom are shown. A correspondence can be considered where the wave functions of a vibrating drum head are for a two-coordinate system and the wave functions for a vibrating sphere are three-coordinate . | Atomic orbital | Wikipedia | 503 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
None of the other sets of modes in a drum membrane have a central antinode, and in all of them the center of the drum does not move. These correspond to a node at the nucleus for all non-s orbitals in an atom. These orbitals all have some angular momentum, and in the planetary model, they correspond to particles in orbit with eccentricity less than 1.0, so that they do not pass straight through the center of the primary body, but keep somewhat away from it.
In addition, the drum modes analogous to p and d modes in an atom show spatial irregularity along the different radial directions from the center of the drum, whereas all of the modes analogous to s modes are perfectly symmetrical in radial direction. The non-radial-symmetry properties of non-s orbitals are necessary to localize a particle with angular momentum and a wave nature in an orbital where it must tend to stay away from the central attraction force, since any particle localized at the point of central attraction could have no angular momentum. For these modes, waves in the drum head tend to avoid the central point. Such features again emphasize that the shapes of atomic orbitals are a direct consequence of the wave nature of electrons.
Orbital energy
In atoms with one electron (hydrogen-like atom), the energy of an orbital (and, consequently, any electron in the orbital) is determined mainly by . The orbital has the lowest possible energy in the atom. Each successively higher value of has a higher energy, but the difference decreases as increases. For high , the energy becomes so high that the electron can easily escape the atom. In single electron atoms, all levels with different within a given are degenerate in the Schrödinger approximation, and have the same energy. This approximation is broken slightly in the solution to the Dirac equation (where energy depends on and another quantum number ), and by the effect of the magnetic field of the nucleus and quantum electrodynamics effects. The latter induce tiny binding energy differences especially for s electrons that go nearer the nucleus, since these feel a very slightly different nuclear charge, even in one-electron atoms; see Lamb shift. | Atomic orbital | Wikipedia | 438 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
In atoms with multiple electrons, the energy of an electron depends not only on its orbital, but also on its interactions with other electrons. These interactions depend on the detail of its spatial probability distribution, and so the energy levels of orbitals depend not only on but also on . Higher values of are associated with higher values of energy; for instance, the 2p state is higher than the 2s state. When , the increase in energy of the orbital becomes so large as to push the energy of orbital above the energy of the s orbital in the next higher shell; when the energy is pushed into the shell two steps higher. The filling of the 3d orbitals does not occur until the 4s orbitals have been filled.
The increase in energy for subshells of increasing angular momentum in larger atoms is due to electron–electron interaction effects, and it is specifically related to the ability of low angular momentum electrons to penetrate more effectively toward the nucleus, where they are subject to less screening from the charge of intervening electrons. Thus, in atoms with higher atomic number, the of electrons becomes more and more of a determining factor in their energy, and the principal quantum numbers of electrons becomes less and less important in their energy placement.
The energy sequence of the first 35 subshells (e.g., 1s, 2p, 3d, etc.) is given in the following table. Each cell represents a subshell with and given by its row and column indices, respectively. The number in the cell is the subshell's position in the sequence. For a linear listing of the subshells in terms of increasing energies in multielectron atoms, see the section below.
Note: empty cells indicate non-existent sublevels, while numbers in italics indicate sublevels that could (potentially) exist, but which do not hold electrons in any element currently known.
Electron placement and the periodic table
Several rules govern the placement of electrons in orbitals (electron configuration). The first dictates that no two electrons in an atom may have the same set of values of quantum numbers (this is the Pauli exclusion principle). These quantum numbers include the three that define orbitals, as well as the spin magnetic quantum number . Thus, two electrons may occupy a single orbital, so long as they have different values of . Because takes one of only two values ( or ), at most two electrons can occupy each orbital. | Atomic orbital | Wikipedia | 495 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
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