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Modern relativity is based on Einsteinâs two postulates. The first postulate of special relativity is the idea that the laws of physics are the same and can be stated in their simplest form in all inertial frames of reference. The second postulate of special relativity is the idea that the speed of lightccis a consta... | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
The Michelson-Morley experiment demonstrated that the speed of light in a vacuum is independent of the motion of the Earth about the Sun. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
Two events are defined to be simultaneous if an observer measures them as occurring at the same time. They are not necessarily simultaneous to all observersâsimultaneity is not absolute. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
Time dilation is the phenomenon of time passing slower for an observer who is moving relative to another observer. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
Observers moving at a relative velocityvvdo not measure the same elapsed time for an event. Proper timeÎt0Ît0is the time measured by an observer at rest relative to the event being observed. Proper time is related to the timeÎtÎtmeasured by an Earth-bound observer by the equationÎt=Ît01âv2c2=γÎt0,Ît=Ît01â... | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
where | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
The equation relating proper time and time measured by an Earth-bound observer implies that relative velocity cannot exceed the speed of light. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
The twin paradox asks why a twin traveling at a relativistic speed away and then back towards the Earth ages less than the Earth-bound twin. The premise to the paradox is faulty because the traveling twin is accelerating. Special relativity does not apply to accelerating frames of reference. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
Time dilation is usually negligible at low relative velocities, but it does occur, and it has been verified by experiment. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
All observers agree upon relative speed. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
Distance depends on an observerâs motion. Proper lengthL0L0is the distance between two points measured by an observer who is at rest relative to both of the points. Earth-bound observers measure proper length when measuring the distance between two points that are stationary relative to the Earth. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
Length contractionLLis the shortening of the measured length of an object moving relative to the observerâs frame:L=L01âv2c2=L0γ.L=L01âv2c2=L0γ. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
With classical velocity addition, velocities add like regular numbers in one-dimensional motion:u=v+uâ²u=v+uâ², wherevvis the velocity between two observers,uuis the velocity of an object relative to one observer, anduâ²uâ²is the velocity relative to the other observer. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
Velocities cannot add to be greater than the speed of light. Relativistic velocity addition describes the velocities of an object moving at a relativistic speed:u=v+uâ²1+vuâ²c2u=v+uâ²1+vuâ²c2 | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
An observer of electromagnetic radiation seesrelativistic Doppler effectsif the source of the radiation is moving relative to the observer. The wavelength of the radiation is longer (called a red shift) than that emitted by the source when the source moves away from the observer and shorter (called a blue shift) when t... | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
The law of conservation of momentum is valid whenever the net external force is zero and for relativistic momentum. Relativistic momentumppis classical momentum multiplied by the relativistic factorγγ. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
p=γmup=γmu, wheremmis the rest mass of the object,uuis its velocity relative to an observer, and the relativistic factorγ=11âu2c2γ=11âu2c2. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
At low velocities, relativistic momentum is equivalent to classical momentum. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
Relativistic momentum approaches infinity asuuapproachescc. This implies that an object with mass cannot reach the speed of light. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
Relativistic momentum is conserved, just as classical momentum is conserved. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
Relativistic energy is conserved as long as we define it to include the possibility of mass changing to energy. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
Total Energy is defined as:E=γmc2E=γmc2, whereγ=11âv2c2γ=11âv2c2. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
Rest energy isE0=mc2E0=mc2, meaning that mass is a form of energy. If energy is stored in an object, its mass increases. Mass can be destroyed to release energy. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
We do not ordinarily notice the increase or decrease in mass of an object because the change in mass is so small for a large increase in energy. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
The relativistic work-energy theorem isWnet=EâE0=γmc2âmc2=γâ1mc2Wnet=EâE0=γmc2âmc2=γâ1mc2. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
Relativistically,Wnet=KErelWnet=KErel,
whereKErelKErelis the relativistic kinetic energy. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
Relativistic kinetic energy isKErel=γâ1mc2KErel=γâ1mc2, whereγ=11âv2c2γ=11âv2c2. At low velocities, relativistic kinetic energy reduces to classical kinetic energy. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
No object with mass can attain the speed of lightbecause an infinite amount of work and an infinite amount of energy input is required to accelerate a mass to the speed of light. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
The equationE2=(pc)2+(mc2)2E2=(pc)2+(mc2)2relates the relativistic total energyEEand the relativistic momentumpp. At extremely high velocities, the rest energymc2mc2becomes negligible, andE=pcE=pc. | https://openstax.org/books/college-physics-2e/pages/28-section-summary |
atomic spectra : the electromagnetic emission from atoms and molecules | https://openstax.org/books/college-physics-2e/pages/29-glossary |
binding energy : also called thework function; the amount of energy necessary to eject an electron from a material | https://openstax.org/books/college-physics-2e/pages/29-glossary |
blackbody : an ideal radiator, which can radiate equally well at all wavelengths | https://openstax.org/books/college-physics-2e/pages/29-glossary |
blackbody radiation : the electromagnetic radiation from a blackbody | https://openstax.org/books/college-physics-2e/pages/29-glossary |
bremsstrahlung : German forbraking radiation; produced when electrons are decelerated | https://openstax.org/books/college-physics-2e/pages/29-glossary |
characteristic x rays : x rays whose energy depends on the material they were produced in | https://openstax.org/books/college-physics-2e/pages/29-glossary |
Compton effect : the phenomenon whereby x rays scattered from materials have decreased energy | https://openstax.org/books/college-physics-2e/pages/29-glossary |
correspondence principle : in the classical limit (large, slow-moving objects), quantum mechanics becomes the same as classical physics | https://openstax.org/books/college-physics-2e/pages/29-glossary |
de Broglie wavelength : the wavelength possessed by a particle of matter, calculated byλ=h/pλ=h/p | https://openstax.org/books/college-physics-2e/pages/29-glossary |
gamma ray : alsoγγ-ray; highest-energy photon in the EM spectrum | https://openstax.org/books/college-physics-2e/pages/29-glossary |
Heisenbergâs uncertainty principle : a fundamental limit to the precision with which pairs of quantities (momentum and position, and energy and time) can be measured | https://openstax.org/books/college-physics-2e/pages/29-glossary |
infrared radiation : photons with energies slightly less than red light | https://openstax.org/books/college-physics-2e/pages/29-glossary |
ionizing radiation : radiation that ionizes materials that absorb it | https://openstax.org/books/college-physics-2e/pages/29-glossary |
microwaves : photons with wavelengths on the order of a micron (μmμm) | https://openstax.org/books/college-physics-2e/pages/29-glossary |
particle-wave duality : the property of behaving like either a particle or a wave; the term for the phenomenon that all particles have wave characteristics | https://openstax.org/books/college-physics-2e/pages/29-glossary |
photoelectric effect : the phenomenon whereby some materials eject electrons when light is shined on them | https://openstax.org/books/college-physics-2e/pages/29-glossary |
photon : a quantum, or particle, of electromagnetic radiation | https://openstax.org/books/college-physics-2e/pages/29-glossary |
photon energy : the amount of energy a photon has;E=hfE=hf | https://openstax.org/books/college-physics-2e/pages/29-glossary |
photon momentum : the amount of momentum a photon has, calculated byp=hλ=Ecp=hλ=Ec | https://openstax.org/books/college-physics-2e/pages/29-glossary |
Planckâs constant : h=6.626Ã10â34Jâsh=6.626Ã10â34Jâs | https://openstax.org/books/college-physics-2e/pages/29-glossary |
probability distribution : the overall spatial distribution of probabilities to find a particle at a given location | https://openstax.org/books/college-physics-2e/pages/29-glossary |
quantized : the fact that certain physical entities exist only with particular discrete values and not every conceivable value | https://openstax.org/books/college-physics-2e/pages/29-glossary |
quantum mechanics : the branch of physics that deals with small objects and with the quantization of various entities, especially energy | https://openstax.org/books/college-physics-2e/pages/29-glossary |
ultraviolet radiation : UV; ionizing photons slightly more energetic than violet light | https://openstax.org/books/college-physics-2e/pages/29-glossary |
uncertainty in energy : lack of precision or lack of knowledge of precise results in measurements of energy | https://openstax.org/books/college-physics-2e/pages/29-glossary |
uncertainty in momentum : lack of precision or lack of knowledge of precise results in measurements of momentum | https://openstax.org/books/college-physics-2e/pages/29-glossary |
uncertainty in position : lack of precision or lack of knowledge of precise results in measurements of position | https://openstax.org/books/college-physics-2e/pages/29-glossary |
uncertainty in time : lack of precision or lack of knowledge of precise results in measurements of time | https://openstax.org/books/college-physics-2e/pages/29-glossary |
visible light : the range of photon energies the human eye can detect | https://openstax.org/books/college-physics-2e/pages/29-glossary |
x ray : EM photon betweenγγ-ray and UV in energy | https://openstax.org/books/college-physics-2e/pages/29-glossary |
The first indication that energy is sometimes quantized came from blackbody radiation, which is the emission of EM radiation by an object with an emissivity of 1. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
Planck recognized that the energy levels of the emitting atoms and molecules were quantized, with only the allowed values ofE=n+12hf,E=n+12hf,wherennis any non-negative integer (0, 1, 2, 3, â¦). | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
hhis Planckâs constant, whose value ish=6.626Ã10â34Jâs.h=6.626Ã10â34Jâs. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
Thus, the oscillatory absorption and emission energies of atoms and molecules in a blackbody could increase or decrease only in steps of sizeÎE=hfÎE=hfwhereffis the frequency of the oscillatory nature of the absorption and emission of EM radiation. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
Another indication of energy levels being quantized in atoms and molecules comes from the lines in atomic spectra, which are the EM emissions of individual atoms and molecules. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
The photoelectric effect is the process in which EM radiation ejects electrons from a material. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
Einstein proposed photons to be quanta of EM radiation having energyE=hfE=hf, whereffis the frequency of the radiation. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
All EM radiation is composed of photons. As Einstein explained, all characteristics of the photoelectric effect are due to the interaction of individual photons with individual electrons. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
The maximum kinetic energyKEeKEeof ejected electrons (photoelectrons) is given byKEe=hfâ BEKEe=hfâ BE, wherehfhfis the photon energy and BE is the binding energy (or work function) of the electron to the particular material. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
Photon energy is responsible for many characteristics of EM radiation, being particularly noticeable at high frequencies. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
Photons have both wave and particle characteristics. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
Photons have momentum, given byp=hλp=hλ, whereλλis the photon wavelength. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
Photon energy and momentum are related byp=Ecp=Ec, whereE=hf=hc/λE=hf=hc/λfor a photon. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
EM radiation can behave like either a particle or a wave. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
This is termed particle-wave duality. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
Particles of matter also have a wavelength, called the de Broglie wavelength, given byλ=hpλ=hp, whereppis momentum. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
Matter is found to have the sameinterference characteristicsas any other wave. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
Matter is found to have the same interference characteristics as any other wave. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
There is now a probability distribution for the location of a particle rather than a definite position. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
Another consequence of the wave character of all particles is the Heisenberg uncertainty principle, which limits the precision with which certain physical quantities can be known simultaneously. For position and momentum, the uncertainty principle isÎxÎpâ¥h4ÏÎxÎpâ¥h4Ï, whereÎxÎxis the uncertainty in position ... | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
For energy and time, the uncertainty principle isÎEÎtâ¥h4ÏÎEÎtâ¥h4ÏwhereÎEÎEis the uncertainty in energy andÎtÎtis the uncertainty in time. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
These small limits are fundamentally important on the quantum-mechanical scale. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
The particle-wave duality refers to the fact that all particlesâthose with mass and those without massâhave wave characteristics. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
This is a further connection between mass and energy. | https://openstax.org/books/college-physics-2e/pages/29-section-summary |
angular momentum quantum number : a quantum number associated with the angular momentum of electrons | https://openstax.org/books/college-physics-2e/pages/30-glossary |
atom : basic unit of matter, which consists of a central, positively charged nucleus surrounded by negatively charged electrons | https://openstax.org/books/college-physics-2e/pages/30-glossary |
atomic de-excitation : process by which an atom transfers from an excited electronic state back to the ground state electronic configuration; often occurs by emission of a photon | https://openstax.org/books/college-physics-2e/pages/30-glossary |
atomic excitation : a state in which an atom or ion acquires the necessary energy to promote one or more of its electrons to electronic states higher in energy than their ground state | https://openstax.org/books/college-physics-2e/pages/30-glossary |
atomic number : the number of protons in the nucleus of an atom | https://openstax.org/books/college-physics-2e/pages/30-glossary |
Bohr radius : the mean radius of the orbit of an electron around the nucleus of a hydrogen atom in its ground state | https://openstax.org/books/college-physics-2e/pages/30-glossary |
Brownian motion : the continuous random movement of particles of matter suspended in a liquid or gas | https://openstax.org/books/college-physics-2e/pages/30-glossary |
cathode-ray tube : a vacuum tube containing a source of electrons and a screen to view images | https://openstax.org/books/college-physics-2e/pages/30-glossary |
double-slit interference : an experiment in which waves or particles from a single source impinge upon two slits so that the resulting interference pattern may be observed | https://openstax.org/books/college-physics-2e/pages/30-glossary |
energies of hydrogen-like atoms : Bohr formula for energies of electron states in hydrogen-like atoms:En=âZ2n2E0(n=1, 2, 3,â¦)En=âZ2n2E0(n=1, 2, 3,â¦) | https://openstax.org/books/college-physics-2e/pages/30-glossary |
energy-level diagram : a diagram used to analyze the energy level of electrons in the orbits of an atom | https://openstax.org/books/college-physics-2e/pages/30-glossary |
fine structure : the splitting of spectral lines of the hydrogen spectrum when the spectral lines are examined at very high resolution | https://openstax.org/books/college-physics-2e/pages/30-glossary |
fluorescence : any process in which an atom or molecule, excited by a photon of a given energy, de-excites by emission of a lower-energy photon | https://openstax.org/books/college-physics-2e/pages/30-glossary |
hologram : meansentire picture(from the Greek wordholo, as in holistic), because the image produced is three dimensional | https://openstax.org/books/college-physics-2e/pages/30-glossary |
holography : the process of producing holograms | https://openstax.org/books/college-physics-2e/pages/30-glossary |
hydrogen spectrum wavelengths : the wavelengths of visible light from hydrogen; can be calculated by1λ=R1nf2â1ni21λ=R1nf2â1ni2 | https://openstax.org/books/college-physics-2e/pages/30-glossary |
hydrogen-like atom : any atom with only a single electron | https://openstax.org/books/college-physics-2e/pages/30-glossary |
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