index int64 0 999 | image stringlengths 4.4k 871k | question stringlengths 189 2.04k | answer stringclasses 4
values | category stringclasses 6
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values | embedding listlengths 4.1k 4.1k |
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500 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEWAfwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An experiment was performed in which neutrons were shot through two slits spaced \(0.10\text{ nm}\) apart and detected \(3.5\text{ m}\) behind the slits. Figure shows the detector output. To one significant figure, what was the speed of the neutrons?Please directly answer the question and provide the correct OPTION LET... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0341796875,
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501 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEMAbYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the probability density for an electron that has passed through an experimental apparatus. If \( 1.0 \times 10^6 \) electrons are used. What is the expected number that will land in a \( 0.010\text{-mm} \) wide strip at \( x = 2.000\text{ mm} \)?Please directly answer the question and provide the correct O... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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502 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEiAcIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the probability density for an electron that has passed through an experimental apparatus. What is the probability that the electron will land in a \( 0.010\text{-mm} \)-wide strip at \( x = 0.000\text{ mm} \)?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D.... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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503 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEQAdYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure is a graph of \( |\psi(x)|^2 \) for a neutron. What is the probability that the neutron is located at a posi- tion with \( |x| \ge 2\text{ fm} \)?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.65 B: 0.55 C: 0.75 D: 0.50 | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.026123046875,
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504 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACgAbwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows a pulse train. What is the maximum pulse-transmission rate (pulses per second) through an electronics system with a \( 200 \text{ kHz} \) bandwidth? (This is the bandwidth allotted to each FM radio station.)Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OP... | C | Modern Physics | Quantum Phenomena | ['Numerical Reasoning'] | [
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505 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEaAbQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows \( |\psi(x)|^2 \) for the electrons in an experiment. If \( 10^4 \) electrons are detected, how many are expected to land in the interval \( -0.30 \text{ cm} \leq x \leq 0.30 \text{ cm} \)?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 500 B: 10... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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506 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGMAb4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the wave function of a particle. The wave function is zero outside this region. Calculate the probability of finding the particle in the interval \( -2.0 \text{ mm} \leq x \leq 2.0 \text{ mm} \).Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.1... | C | Modern Physics | Quantum Phenomena | ['Numerical Reasoning', 'Physical Model Grounding Reasoning'] | [
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507 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFYAbwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows dust particles (\( m = 1.0 \times 10^{-15} \text{ kg} \)) in a vacuum chamber. The dust particles are released from rest above a hole, fall through the hole (there's just barely room for the particles to go through), and land on a detector below. Quantum effects would be noticeable if the detection-circle ... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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508 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADgAZgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the wave function of an electron in a rigid box. The electron energy is \( 6.0 \text{ eV} \). How long is the box?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 0.5 \text{ nm} \) B: \( 3.0 \text{ nm} \) C: \( 1.0 \text{ nm} \) D: \( 2.0 \text... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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509 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAH4A5gDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A spaceship flies past earth. A crew member on board the spaceship measures its length, obtaining the value as shown in figure. What length do observers measure on earth?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 35.1 \text{ m} \) B: \( 27.7 \text{ m}... | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
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510 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFeA4ADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Let the earth and spaceship reference frames be \( S \) and \( S' \), respectively as shown in figure; their relative velocity is \( u = 0.900c \). We are given the probe velocity \( v'_x = 0.700c \) with respect to \( S' \), and the target variable is the velocity \( v_x \) of the probe relative to \( S \).Please dire... | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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511 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHWAeQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Two protons are initially speeds in opposite directions. They continue to exist after a head-on collision that also produces a neutral pion of mass as shown in figure. If all three particles are at rest after the collision, find the initial speed of the protons. Energy is conserved in the collision.Please directly answ... | D | Modern Physics | Particle Physics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
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512 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACoAwIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An enemy spaceship is moving toward your starfighter with a speed, as measured in your frame, of \( 0.400c \). The enemy ship fires a missile toward you at a speed of \( 0.700c \) relative to the enemy ship as shown in figure. If you measure that the enemy ship is \( 8.00 \times 10^6 \) km away from you when the missil... | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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513 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADaAXYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The starships of the Solar Federation are marked with the symbol of the federation, a circle, while starships of the Denebian Empire are marked with the empire's symbol, an ellipse whose major axis is 1.40 times longer than its minor axis as shown in figure. How fast, relative to an observer, does an empire ship have t... | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
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514 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFWAY4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Many of the stars in the sky are actually binary stars, in which two stars orbit about their common center of mass. If the orbital speeds of the stars are high enough, the motion of the stars can be detected by the Doppler shifts of the light they emit. Stars for which this is the case are called \emph{spectroscopic bi... | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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515 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF2AkwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The graph in figure shows the stopping potential as a function of the frequency of the incident light falling on a metal surface. Find the photoelectric work function for this metal.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 5.6 \text{ eV} \) B: \( 2.... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.046630859375,
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516 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD+AxoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | When a certain photoelectric surface is illuminated with light of different wavelengths, the following stopping potentials are observed as shown in figure:Plot the stopping potential on the vertical axis against the frequency of the light on the horizontal axis. Determine the value of Planck's constant \( h \) (assumin... | D | Modern Physics | Quantum Phenomena | ['Numerical Reasoning', 'Physical Model Grounding Reasoning'] | [
0.033447265625,
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517 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE+AmgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A hypothetical atom is shown in figure. What is the highest frequencies of the spectral lines this atom can emit when excited?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 9.16 \times 10^{14} \) B: \( 2.42 \times 10^{14} \) C: \( 5.50 \times 10^{14} \) D... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
0.0086669921875,
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518 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFCAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | `The energy-level scheme for the hypothetical one-electron element Searsium is shown in figure. The potential energy is taken to be zero for an electron at an infinite distance from the nucleus. Photons emitted in the Searsium transitions \( n = 3 \to n = 2 \) and \( n = 3 \to n = 1 \) will eject photoelectrons from an... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0380859375,
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519 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHeAZoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In a set of experiments on a hypothetical one-electron atom, you measure the wavelengths of the photons emitted from transitions ending in the ground state \( n = 1 \), as shown in the energy-level diagram in figure. You also observe that it takes \( 17.50 \text{ eV} \) to ionize this atom. If an electron made a transi... | D | Modern Physics | Quantum Phenomena | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0181884765625,
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520 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFYAWgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In a simple model for a radioactive nucleus, an alpha particle } \( m = 6.64 \times 10^{-27} \text{ kg} \) \text{ is trapped by a square barrier that has width } \( 2.0 \text{ fm} \) \text{ and height } \( 30.0 \text{ MeV} \) What is the tunneling probability when the alpha particle encounters the barrier if its kineti... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.02392578125,
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521 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAESAXIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Consider a potential well defined as \( U(x) = \infty \) for \( x < 0 \), \( U(x) = 0 \) for \( 0 < x < L \), and \( U(x) = U_0 > 0 \) for \( x > L \) as shown in figure. Consider a particle with mass \( m \) and kinetic energy \( E < U_0 \) that is trapped in the well. The wave function must remain finite as \( x \to ... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.0252685546875,
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522 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACiApYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Van der Waals bonds arise from the interaction between two permanent or induced electric dipole moments in a pair of atoms or molecules. Consider two identical dipoles, separated by a distance \(d\) and oriented as shown in figure. Calculate the electric potential energy, expressed in terms of the electric dipole momen... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.007171630859375,
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523 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADoAaQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The truck in figure is moving at a speed of \(10.0 \, \text{m/s}\) relative to the ground. The person on the truck throws a baseball in the backward direction at a speed of \(20.0 \, \text{m/s}\) relative to the truck. What is the velocity of the baseball as measured by the observer on the ground?Please directly answer... | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.026611328125,
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524 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE2AW4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The speed of the Earth in its orbit is \(29.8 \, \text{km/s}\). If that is the magnitude of the velocity \( \vec{v} \) of the ether wind in figure. Find the angle \( \phi \) between the velocity of light \( \vec{c} \) in vacuum and the resultant velocity of light if there were an ether.Please directly answer the questi... | D | Modern Physics | Relativity | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.015380859375,
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525 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHSATIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Police radar detects the speed of a car as shown in figure. Microwaves of a precisely known frequency are broadcast toward the car. The moving car reflects the microwaves with a Doppler shift. The reflected waves are received and combined with an attenuated version of the transmitted wave. Beats occur between the two m... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.0322265625,
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526 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADcATIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A moving rod is observed to have a length of \( \ell = 2.00 \, \text{m} \) and to be oriented at an angle of \( \theta = 30.0^\circ \) with respect to the direction of motion as shown in figure. The rod has a speed of \( 0.995c \). What is the orientation angle in the proper frame?Please directly answer the question an... | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.02587890625,
0.01312255859375,
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527 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEIApADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An enemy spacecraft moves at a speed of \( v = 0.800c \) as shown in figure. A galactic patrol spacecraft pursues at a speed of \( u = 0.900c \) relative to the Earth. Observers on the Earth measure the patrol craft to be overtaking the enemy craft at a relative speed of \( 0.100c \). With what speed is the patrol craf... | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0302734375,
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0.0084228515625,
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528 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADqAbgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An observer in a coasting spacecraft moves toward a mirror at speed \( v = 0.650c \) relative to the reference frame labeled S in figure. The mirror is stationary with respect to S. A light pulse emitted by the spacecraft travels toward the mirror and is reflected back to the spacecraft. The spacecraft is a distance \(... | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0167236328125,
0.000644683837890625,
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529 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFGApIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Owen and Dina are at rest in frame S\( '\), which is moving with respect to frame S. They play a game of catch while Ed, at rest in frame S, watches the action as shown in figure. Owen throws the ball to Dina. what time interval is required for the ball to reach Dina?Please directly answer the question and provide the ... | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.035888671875,
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0... |
530 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF8Ap4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A photon scatters off a free electron at A as shown in figure, producing a second photon. This photon then scatters off another free electron at B, producing a third photon. Determine the value of \( \Delta \lambda = \lambda'' - \lambda \).Please directly answer the question and provide the correct OPTION LETTER ONLY, ... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.021240234375,
0.0098876953125,
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0.0115966796875,
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0.00994873046875,
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0.01953125,
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0.043701171875,
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0.002471923828125,
... |
531 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD6AeIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A photon having energy \( E_0 = 0.880 \text{ MeV} \) is scattered by a free electron initially at rest as shown in figure. Determine the momentum of the scattered electron.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 9.81 \times 10^{-23} \text{ kg} \cdo... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.017578125,
0.00750732421875,
-0.00095367431640625,
0.0247802734375,
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0.032470703125,
0.0036163330078125,
0.0194091796875,
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0.01318359375,
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0.0302734375,
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0.00421142578125,
0.0179443359375,
0.00732421875,
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532 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFwAmgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In the Davisson-Germer experiment, 54.0-eV electrons were diffracted from a nickel lattice. If the first maximum in the diffraction pattern was observed at \( \phi = 50.0^\circ \) as shown in figure. What was the lattice spacing \( a \) between the vertical columns of atoms in the figure?Please directly answer the ques... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0196533203125,
0.0101318359375,
-0.01416015625,
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0.004425048828125,
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0.0283203125,
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0.0028533935546875,
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... |
533 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADwAaIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An electron with kinetic energy \( E = 5.00 \text{ eV} \) is incident on a barrier of width \( L = 0.200 \text{ nm} \) and height \( U = 10.0 \text{ eV} \) as shown in figure. What is the probability that the electron tunnels through the barrier?Please directly answer the question and provide the correct OPTION LETTER ... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.0233154296875,
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0.00154876708984375,
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0.044189453125,
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0.00537109375,
-0.040283203125,
0.0118408203125,
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0.02490234375,
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0.0024261474609375,
0.0052490234375,
0.01953125,
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534 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADsAawDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Particles incident from the left in figure are confronted with a step in potential energy. The particles have energy \( E \). Classically, all the particles would continue moving forward with reduced speed. According to quantum mechanics, however, a fraction of the particles are reflected at the step. Find its probabil... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.018798828125,
-0.01446533203125,
-0.00022411346435546875,
-0.00096893310546875,
0.001251220703125,
0.01470947265625,
0.00146484375,
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0.01025390625,
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0.0296630859375,
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0.00860595703125,
0.0110473632812... |
535 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACkAWgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Consider a "crystal"consisting of two fixed ions of charge \( +e \) and two electrons as shown in figure. Find the value of \( d \) for which the total energy is a minimum.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 62.1 pm B: 54.4 pm C: 21.8 pm D: 49.9 p... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.017333984375,
0.0089111328125,
0.0002689361572265625,
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0.01214599609375,
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0.01611328125,
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536 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEKAZYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The Balmer series for the hydrogen atom corresponds to electronic transitions that terminate in the state with quantum number \( n = 2 \) as shown in figure. Consider the photon of longest wavelength corresponding to a transition shown in the figure. Find its wavelength.Please directly answer the question and provide t... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0064697265625,
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0.004852294921875,
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0.0035400390625,
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-0.027587890625,
-0.0034942626953125,
-0.010498046875,
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537 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD+AVoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A helium--neon laser can produce a green laser beam instead of a red one. Figure shows the transitions involved to form the red beam and the green beam. After a population inversion is established, neon atoms make a variety of downward transitions in falling from the state labeled \( E_4^* \) down eventually to level \... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0238037109375,
0.0068359375,
0.0169677734375,
-0.0185546875,
0.01080322265625,
0.0157470703125,
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0.0034637451171875,
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0.01904296875,
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0.045654296875,
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0.012939453125,
0.0033111572265625,
0.009033203125,
-0.01745605... |
538 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEwAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure is a model of a benzene molecule. All atoms lie in a plane, and the carbon atoms (\( m_{\text{C}} = 1.99 \times 10^{-26} \text{ kg} \)) form a regular hexagon, as do the hydrogen atoms (\( m_{\text{H}} = 1.67 \times 10^{-27} \text{ kg} \)). Calculate the moment of inertia of the molecule about an axis perpendicu... | D | Modern Physics | Quantum Phenomena | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.00848388671875,
0.0020904541015625,
-0.0211181640625,
-0.0115966796875,
-0.0211181640625,
0.03125,
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0.0294189453125,
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0.0341796875,
-0.01025390625,
-0.00787353515625,
0.0036468505859375,
-0.0015106201171875,
-0... |
539 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIeAZwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Assume a photomultiplier tube for detecting radiation has seven dynodes with potentials of \(100, 200, 300, \ldots, 700 \text{ V}\) as shown in figure. The average energy required to free an electron from the dynode surface is \(10.0 \text{ eV}\). Assume only one electron is incident and the tube functions with \(100\%... | D | Modern Physics | Quantum Phenomena | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.04443359375,
0.0159912109375,
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-0.0074462890625,
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0.0279541015625,
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0.015625,
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0.0184326171875,
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0.0286865234375,
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0.0135498046875,
0.005859375,
-0.002899169921875,
-0.03955078125... |
540 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEsAY4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The particle decay \(\Sigma^+ \rightarrow \pi^+ + n\) is observed in a bubble chamber. Figure represents the curved tracks of the particles \(\Sigma^+\) and \(\pi^+\) and the invisible track of the neutron in the presence of a uniform magnetic field of \(1.15 \text{ T}\) directed out of the page. The measured radii of ... | D | Modern Physics | Particle Physics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.02880859375,
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0.0264892578125,
0.0078125,
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-0.035888671875,
0.0230712890625,
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0.0400390625,
-0.0101318359375,
-0.01226806640625,
0.00579833984375,
0.006439208984375,
-0.0... |
541 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAImA7YDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | As shown in figure Find the probabilities of the measurements shown in figure, assuming that the first Stern-Gerlach analyzer is aligned along the direction \(\hat{\mathbf{n}}\) defined by the angles \(\theta = 2\pi/3\) and \(\phi = \pi/4\).Please directly answer the question and provide the correct OPTION LETTER ONLY,... | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.013671875,
0.00799560546875,
0.004730224609375,
0.015869140625,
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0.015625,
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0.031005859375,
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0.030517578125,
-0.01708984375,
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0.0220947265625,
0.007293701171875,
-0.038574218... |
542 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEqBD4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A beam of spin-\(1/2\) particles is sent through a series of three Stern-Gerlach analyzers, as shown in figure. The second Stern-Gerlach analyzer is aligned along the \(\hat{n}\) direction, which makes an angle \(\theta\) in the \(x\)-\(z\) plane with respect to the \(z\)-axis. Find the probability that particles trans... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
-0.000457763671875,
0.0211181640625,
-0.006500244140625,
-0.0177001953125,
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0.0030364990234375,
0.00927734375,
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0.01025390625,
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0.0135498046875,
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0.005523681640625,
0.01513671875,
0.0019378662109375,
-0.0... |
543 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADsBCQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A spin-\(1/2\) particle with a magnetic moment is prepared in the state \(|-\rangle_x\) and is subject to a uniform applied magnetic field \(\mathbf{B} = B_0 \hat{z}\). Find the probability of measuring spin up in the \(x\)-direction after a time \(t\). This experiment is depicted in figure.Please directly answer the q... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
0.00439453125,
0.017578125,
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0.00096893310546875,
0.01123046875,
0.0108642578125,
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0.025634765625,
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0.00128173828125,
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0.01348876953125,
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544 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGIAmYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Consider a potential energy step as shown in figure with a beam of particles incident from the left. Calculate the reflection coefficient for the case where the energy of the incident particles is greater than the height of the stepPlease directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A,... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.0224609375,
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0.00701904296875,
-0.... |
545 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFMAx4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An infinite square well, shown in figure, is perturbed by an additional potential energy term, with the resultant well shown in figure. Find the first-order corrections to the energies.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \(\frac{V_0}{7}\) B: \(\fr... | D | Modern Physics | Quantum Phenomena | ['Numerical Reasoning', 'Physical Model Grounding Reasoning'] | [
0.030029296875,
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0.0034942626953125,
0.027587890625,
0.013671875,
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0.01318359375,
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0.00811767578125,
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546 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHyAhIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Consider an infinite square well potential with walls at \(x = 0\) and \(x = L\); that is,
\(V(x) = 0\) for \(0 < x < L\); \(V(x) = \infty\) otherwise. Now impose a perturbation on this potential of the form \(H' = L V_0 \delta(x - L/2)\), where \(\delta(x)\) is the Dirac delta function. Now consider the case where we ... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.034423828125,
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0.0250244140625,
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547 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFEApoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Two spacecraft, A and B, are observed from the ground to be flying as shown in figure. What is the velocity of spacecraft A relative to spacecraft B?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \(0.135c\) B: \(1.301c\)
C: \(1.700c\) D: \(0.987c\) | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0234375,
0.00811767578125,
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-0.0233154296875,
0.01434326171875,
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-0.00946044921875,
-0.044921875,
0.0235595703125,
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0.029296875,
-0.021728515625,
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0.0196533203125,
0.002166748046875,
-0.00... |
548 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADOAm4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A photon of frequency \(\nu\) undergoes elastic scattering from a stationary free electron, as shown in the figure. The energy of the photon is \(h\nu\). Considering the photon-electron system, use momentum conservation, energy conservation, and the relativistic energy-momentum relation to derive the relationship betwe... | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0033111572265625,
0.0069580078125,
-0.0004119873046875,
-0.01092529296875,
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0.01397705078125,
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-0.0546875,
0.0224609375,
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0.013427734375,
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549 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHMAgQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The curve shown in the figure was obtained in a photoelectric effect experiment. Determine Planck's constant \(h\) from the data in the figure.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \[ 5.34 \times 10^{-34} \text{ J} \cdot \text{s} \] B: \[ 4.11 \time... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.0164794921875,
0.01214599609375,
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0.029541015625,
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0.017578125,
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0.0277099609375,
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0.007293701171875,
0.01470947265625,
-0... |
550 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF8Am4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A particle is confined between two impenetrable walls as shown in the figure. The wave function describing the particle's state is $\psi = cx(l-x)$, where $c$ is an undetermined constant. Calculate the probability of finding the particle in the interval from $0$ to $\frac{1}{3}l$.Please directly answer the question and... | D | Modern Physics | Quantum Phenomena | ['Numerical Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0390625,
0.01251220703125,
0.02197265625,
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0.019775390625,
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0.003173828125,
0.0283203125,
-0.0269775390625... |
551 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAa4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An atom of uranium (\( m = 3.9529 \times 10^{-25} \) kg) at rest decays spontaneously into an atom of helium (\( m = 6.6465 \times 10^{-27} \) kg) and an atom of thorium (\( m = 3.8864 \times 10^{-25} \) kg). The helium atom is observed to move in the positive \( x \) direction with a velocity of \( 1.423 \times 10^7 \... | D | Modern Physics | Nuclear Physics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0191650390625,
-0.00225830078125,
-0.01080322265625,
0.00537109375,
0.00396728515625,
0.01251220703125,
0.004913330078125,
0.01080322265625,
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0.0108642578125,
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0.002960205078125,
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0.009033203125,
-... |
552 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAB0ARwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An observer \( O \) is standing on a platform on a space station. A rocket passes at a relative moving parallel to the edge of the platform. The observer \( O \) notes that the front and back of the rocket simultaneously line up with the ends of the platform at a particular instant as shown in figure. According to \( O... | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.036865234375,
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0.00054168701171875,
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0.031494140625,
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0.003936767578125,
... |
553 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACMAaQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A spaceship moving away from the Earth fires a missile parallel to its direction of motion as shown in figure. What is the speed of the missile as measured by an observer on the Earth?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 0.60c \) B: \( 0.80c \) ... | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.027587890625,
0.009765625,
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0.006744384765625,
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0.01123046875,
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0.031982421875,
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0.012451171875,
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0.0034637451171875,
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-0.0095825195... |
554 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIkAbgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In the reaction \( \text{K}^- + \text{p} \rightarrow \Lambda^0 + \pi^0 \), a charged K meson (mass \( 493.7 \text{ MeV}/c^2 \)) collides with a proton (\( 938.3 \text{ MeV}/c^2 \)) at rest, producing a lambda particle (\( 1115.7 \text{ MeV}/c^2 \)) and a neutral pi meson (\( 135.0 \text{ MeV}/c^2 \)), as represented in... | D | Modern Physics | Particle Physics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0277099609375,
0.000606536865234375,
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0.02001953125,
0.01312255859375,
0.015869140625,
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0.029296875,
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0.039306640625,
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0.0189208984375,
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555 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFQAqQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The discovery of the antiproton \( \overline{\text{p}} \) (a particle with the same rest energy as a proton, \( 938 \text{ MeV} \), but with the opposite electric charge) took place in 1956 through the following reaction:
\[ \text{p} + \text{p} \rightarrow \text{p} + \text{p} + \text{p} + \overline{\text{p}} \]
in whic... | D | Modern Physics | Particle Physics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0162353515625,
-0.005523681640625,
-0.00011920928955078125,
-0.0027618408203125,
-0.0194091796875,
0.0194091796875,
0.0029144287109375,
0.0108642578125,
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0.02001953125,
-0.025634765625,
0.03173828125,
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0.00799560546875,
0.024780273437... |
556 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADGAaIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Particle A has a rest energy of \( 1192 \text{ MeV} \) and is moving through the laboratory in the positive \( x \) direction. It decays into particle B (rest energy = \( 1116 \text{ MeV} \)) and a photon; particle A disappears in the decay process. The photon moves in a direction at an angle \( \theta \) with the posi... | D | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.017822265625,
0.01165771484375,
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0.03857421875,
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0.0296630859375,
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0.042724609375,
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0.005706787109375,
0.0218505859375,
0.00494384765625,
-0... |
557 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEAAYADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A beam of thermal neutrons emerges from a nuclear reactor and is incident on a crystal as shown in figure. The beam is Bragg scattered from a crystal whose scattering planes are separated by \( 0.247 \text{ nm} \). From the continuous energy spectrum of the beam we wish to select neutrons of energy \( 0.0105 \text{ eV}... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.01214599609375,
0.03466796875,
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-0.012939453125,
0.02001953125,
0.01220703125,
-0.0301513671875,
-0.0264892578125,
-0.020263671875,
0.0135498046875,
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0.0390625,
-0.0208740234375,
0.00750732421875,
0.0147705078125,
-0.00007152557373046875,
-0.0277099... |
558 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAB8AegDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | What is the velocity of each proton relative to the other?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 0.91c \) B: \( 0.82c \) C: \( 0.68c \) D: \( 0.95c \) | D | Modern Physics | Relativity | ['Multi-Formula Reasoning', 'Spatial Relation Reasoning'] | [
0.0263671875,
0.00726318359375,
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0.010498046875,
0.00098419189453125,
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0.0205078125,
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0.033203125,
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0.01263427734375,
0.0169677734375,
0.005218505859375,
0.0058... |
559 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADWAVgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A rectangular box at rest in S' has sides \( a' = 2 \text{ m} \), \( b' = 2 \text{ m} \), and \( c' = 4 \text{ m} \) and is oriented as shown in figure S' moves with \( \beta = 0.65 \) with respect to the laboratory frame S. Compute the volume of the box in S' and in S.Please directly answer the question and provide t... | D | Modern Physics | Relativity | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.045654296875,
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0.00823974609375,
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0.015869140625,
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0.01318359375,
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560 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFWATYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Suppose that a particle with mass \( m \) and energy \( E \) is moving toward the origin of a system \( S \) such that its velocity \( \mathbf{u} \) makes an angle \( \alpha \) with the \( y \) axis as shown in figure. determine the energy \( E' \) of the particle measured by an observer in \( S' \), which moves relat... | D | Modern Physics | Relativity | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.00164031982421875,
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561 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEIAhYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Assuming that the difference between Thomson's calculated \( e/m \) in his second experiment (see Figure 3-19) and the currently accepted value was due entirely to his neglecting the horizontal component of Earth's magnetic field outside the deflection plates. What value for that component does the difference imply? (... | D | Modern Physics | Quantum Phenomena | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.043212890625,
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562 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFeAhgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A small shot of negligible radius hits a stationary smooth, hard sphere of radius \( R \), making an angle \( \beta \) with the normal to the sphere, as shown in figure. It is reflected at an equal angle to the normal. The scattering angle is \( \theta = 180^{\circ} - 2\beta \), as shown. If the incoming intensity of... | D | Modern Physics | Quantum Phenomena | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.01495361328125,
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563 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGqAUYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | If a classical system does not have a constant charge-to-mass ratio throughout the system, the magnetic moment can be written
\[ \mu = g \frac{Q}{2M} L \]
where \( Q \) is the total charge, \( M \) is the total mass, and \( g \neq 1 \). What is \( g\) for a solid sphere (\( I = 2MR^2/5 \)) that has a ring of charge on... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.02099609375,
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564 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIQAzADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An early method testing Maxwell's theoretical prediction for the distribution of molecular speeds is shown in figure. In 1925 Otto Stern used a beam of \(\text{Bi}_2\) molecules emitted from an oven at 850 K. The beam defined by slit \(\text{S}_1\) was admitted into the interior of a rotating drum via slit \(\text{S}_2... | D | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.005828857421875,
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565 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE6BJoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A rocket moves with a speed of 0.60c and forms an angle of $45^{\circ}$ with respect to the x-axis, as determined by an observer O. What is the velocity of the rocket as determined by a second observer O′ moving with a speed of 0.80c along the common x–x′-axis with respect to the observer O?Please directly answer the q... | B | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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566 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF4AogDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Observer O measures the area 3 m$^2$ of an equilateral triangle ABC at rest in his xy-plane. An observer O′ moving relative to O at 0.6c observes the triangle A′B′C′. The triangle symmetry axis forms an angle $\theta = 15^{\circ}$ with respect to the direction x–x′ as measured by observer O What is the area measured by... | B | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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567 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJWA/4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The light from a nearby star is observed to be shifted toward blue by 2%, i.e. $\frac{\Delta \lambda}{\lambda} = -0.02$. How fast is it moving?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.55c B: 0.0198c C: 0.95c D: 10.2c | B | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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568 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGGAowDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A rocket ship of length $L_0 = 240$ m, at rest with respect to an observer O′, travels at a constant velocity $V = 0.6c$ relative to an inertial observer O on the ground. A light source is placed midway in the rocket ship, at point B, between two mirrors, points A and C (see figure 17.4). The light source emits two fla... | B | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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569 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGKBWQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An x-ray photon with energy of 100 keV experiences a ‘head-on’ collision with an electron at rest. Using conservation of momentum and energy, find the recoil velocity of the electron.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.55c B: 0.95c C: 0.32c D: 1... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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570 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADwAa4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Consider a particle of kinetic energy $K$ and a potential barrier steps from 0 to $V_0$ at $x = 0$. Calculate the penetration distance for a 5-eV electron approaching a step barrier of 10 eV.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.55nm B: 0.95nm C: ... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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571 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAMmA24DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Based on the figure. What is the wavelength of a photon required to excite a transition from $l=0$ to $l=1$?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 123\mu\m B: 452\mu\m C: 344\mu\m D: 425\mu\m | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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572 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF0ApgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A certain diode has a reverse bias current of $1.0 \times 10^{-5}$ A. Now this diode is connected in forward bias in the circuit shown below, in series with a resistor and with a constant voltage source. What is the wavelength of a photon required to excite a transition from $l=0$ to $l=1$?Please directly answer the qu... | C | Modern Physics | Quantum Phenomena | [] | [
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573 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIKA14DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows an early proposal for a hydrogen bomb. The fusion fuel is deuterium. The high temperature and particle density needed for fusion are provided by an atomic bomb "trigger" that involves a fission fuel arranged to impress an imploding, compressive shock wave on the deuterium. The fusion reaction is \[ 5\ {}^{... | C | Modern Physics | Nuclear Physics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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574 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIjAgoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows part of the decay scheme on a plot of mass number $A$ versus proton number $Z$; five lines that represent either alpha decay or beta-minus decay connect dots that represent isotopes. What is the isotope at the end of the five decays (as marked with a question mark in figure)?Please directly answer the ques... | C | Modern Physics | Nuclear Physics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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... |
575 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJWApMDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Doping changes the Fermi energy of a semiconductor. Consider silicon. At \( 300\text{K} \) the Fermi level of the pure material is nearly at the mid-point of the gap. Suppose that silicon is doped with donor atoms, each of which has a state \( 0.15\text{eV} \) below the bottom of the silicon conduction band, and suppos... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.017822265625,
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576 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIDAkcDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the decay of parents in a radioactive sample. The axes are scaled by $N_s = 2.00 \times 10^6$ and $t_s = 10.0 \, \text{s}$. What is the activity of the sample at $t = 27.0 \, \text{s}$?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 30Bq B: 120Bq... | C | Modern Physics | Nuclear Physics | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
0.033447265625,
0.0167236328125,
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577 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCALRAkoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Comet stimulated emission. When a comet approaches the Sun, the increased warmth evaporates water from the ice on the surface of the comet nucleus, producing a thin atmosphere of water vapor around the nucleus. Sunlight can then dissociate H\_2O molecules in the vapor to H atoms and OH molecules. The sunlight can also ... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.041748046875,
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578 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCALCAjoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Excited sodium atoms emit two closely spaced spectrum lines called the sodium doublet with wavelengths. This energy difference occurs because the electron's spin magnetic moment can be oriented either parallel or antiparallel to the internal magnetic field associated with the electron's orbital motion.Please directly a... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning'] | [
0.041015625,
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579 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAMlA3MDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Where sunlight shines on the atmosphere of Mars, carbon dioxide molecules at an altitude of about $75 \, \text{km}$ undergo natural laser action. The energy levels involved in the action are shown figure; population inversion occurs between energy levels $E_2$ and $E_1$. At what wave-length does lasing occur?Please dir... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0277099609375,
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580 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGOAUQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure is an energy-level diagram for a fictitious three-dimensional infinite potential well that contains one electron. The number of degenerate states of the levels are indicated. Assume that the electrostatic forces between the electrons are negligible. If we put a total of 22 electrons in the well, what multiple of... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0264892578125,
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581 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFbASMDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure is an energy-level diagram for a fictitious infinite potential well that contains one electron. The number of degenerate states of the levels are indicated. We put a total of 11 electrons in the well. If the electrostatic forces between the electrons can be neglected, what multiple of \( h^2 \!/ 8mL^2 \) gives t... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.032958984375,
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582 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIAAlcDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A diatomic gas molecule consists of two atoms of mass \( m \) separated by a fixed distance \( d \) rotating about an axis. Assuming that its angular momentum is quantized as in the Bohr model for the hydrogen atom, find the possible quantized rotational energies.Please directly answer the question and provide the corr... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.0054931640625,
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583 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAKEAsADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The two-dimensional, infinite corral of figure is square, with edge length $L = 150 \, \text{pm}$. A square probe is centered at $xy$ coordinates $(0.200L, 0.800L)$ and has an $x$ width of $5.00 \, \text{pm}$ and a $y$ width of $5.00 \, \text{pm}$. What is the probability of detection if the electron is in the $E_{1,3}... | C | Modern Physics | Quantum Phenomena | ['Spatial Relation Reasoning', 'Numerical Reasoning'] | [
0.028564453125,
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584 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGwAq8DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | We probe for the electron along a line that bisects \( L_x \) and find three points at which the detection probability is maximum. Those points are separated by \( 2.00\text{nm} \). Then we probe along a line that bisects \( L_y \) and find five points at which the detection probability is maximum. Those points are sep... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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585 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAMrA4QDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An electron is shown traveling rightward toward the trap, in a region with a voltage of \( V_1 = -9.00\,\text{V} \), where it has a kinetic energy of \( 2.00\,\text{eV} \). When the electron enters the trap region, it can become trapped if it gets rid of enough energy by emitting a photon. What is the smallest energy (... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Implicit Condition Reasoning'] | [
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586 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJ6Ap0DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The electron can absorb at the indicated wavelengths: \( \lambda_a = 14.588\,\text{nm} \) and \( \lambda_b = 4.8437\,\text{nm} \) and for any wavelength less than \( \lambda_c = 2.9108\,\text{nm} \). What is the energy of the first excited state?Please directly answer the question and provide the correct OPTION LETTER ... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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587 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAB1A7QDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An electron is trapped in a one-dimensional infinite well and is in its first excited state. Figure indicates the five longest wavelengths of light that the electron could absorb in transitions from this initial state via a single photon absorption: \( \lambda_a = 80.78\,\text{nm} \), \( \lambda_b = 33.66\,\text{nm} \)... | C | Modern Physics | Quantum Phenomena | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0150146484375,
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... |
588 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJnApcDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A light detector has an absorbing area of \( 2.00\times10^{-6}\,\text{m}^2 \) and absorbs 50\% of the incident light, which is at wavelength \( 600\,\text{nm} \). The detector faces an isotropic source, \( 12.0\,\text{m} \) from the source. The energy \( E \) emitted by the source versus time \( t \) is given in figure... | C | Modern Physics | Quantum Phenomena | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
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589 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEWA0IDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, two cruisers fly toward a space station. Relative to the station, cruiser \( A \) has speed \( 0.800c \). Relative to the station, what speed is required of cruiser \( B \) such that its pilot sees \( A \) and the station approach \( B \) at the same speed?Please directly answer the question and provide the ... | C | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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... |
590 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADMAzMDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, three spaceships are in a chase. Relative to an \( x \) axis in an inertial frame (say, Earth frame), their velocities are \( v_A = 0.900c \), \( v_B \), and \( v_C = 0.800c \). What value of \( v_B \) is required such that ships \( A \) and \( C \) approach ship \( B \) with the same speed relative to ship ... | C | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.05029296875,
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0.0101318359375,
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0.031494140625,
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0.0152587890625,
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0.006164550781... |
591 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIrAQoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | One cosmic-ray particle approaches Earth along Earth's north-south axis with a speed toward the geographic north pole, and another approaches with a speed toward the geographic south pole. What is the relative speed of approach of one particle with respect to the other?Please directly answer the question and provide th... | C | Modern Physics | Relativity | ['Numerical Reasoning', 'Physical Model Grounding Reasoning'] | [
0.03173828125,
0.006195068359375,
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0.009765625,
0.0014190673828125,
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... |
592 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCANwA0gDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure gives their spatial separation $\Delta x$ according to the $S$ observer as a function of $\Delta t$ for a range of $\Delta t$ values. The vertical axis scale is set by $\Delta x_a = 10.0 \, \text{m}$. What is $\Delta x'$?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, ... | C | Modern Physics | Relativity | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.036376953125,
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593 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHBA54DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A radar transmitter \( T \) is fixed to a reference frame \( S' \) that is moving to the right with speed \( v \) relative to reference frame \( S \). A mechanical timer (essentially a clock) in frame \( S' \), having a period \( au_0 \) (measured in \( S' \)), causes transmitter \( T \) to emit timed radar pulses, wh... | C | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.02392578125,
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0.00127410888671875,
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0.034912109375,
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0.00384521484375,
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594 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJrAywDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the path taken by a knot in a jet of ionized gas that has been expelled from a galaxy. The knot travels at constant velocity at angle $\theta$ from the direction of Earth. The knot occasionally emits a burst of light, which is eventually detected on Earth. Two bursts are indicated in figure, separated by t... | C | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.030029296875,
0.0103759765625,
-0.00811767578125,
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0.017578125,
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0.0380859375,
0.0037841796875,
0.0137939453125,
0.0252685546875,
-0.00946044921875,
-0.026489257812... |
595 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGIAi0DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure gives the velocity $u'$ of a particle relative to frame $S'$ for a range of values of $v$, where $v$ is the velocity of frame $S'$ relative to a reference frame $S$. The vertical axis scale is set by $u'_a = -0.800c$. What value will \( u' \) have if \( v \rightarrow c \)?Please directly answer the question and ... | C | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
0.04443359375,
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0.0120849609375,
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0.0020751953125,
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0.00006103515625,
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0.018310546875,
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0.005828857421875,
0.0133056640625,
-0.0125732421875,
... |
596 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAH2A48DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure is a graph of intensity versus wavelength for light reaching Earth from galaxy NGC 7319, which is about \( 3 \times 10^8 \) light-years away. The most intense light is emitted by the oxygen in NGC 7319. In a laboratory that emission is at wavelength \( \lambda = 513\,\text{nm} \), but in the light from NGC 7319 ... | C | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0201416015625,
-0.0162353515625,
-0.0206298828125,
-0.0291748046875,
-0.0152587890625,
0.01361083984375,
-0.0037384033203125,
0.0177001953125,
-0.0302734375,
0.012939453125,
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0.038330078125,
-0.0004634857177734375,
0.02294921875,
0.01251220703125,
0.005645751953125,
-... |
597 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGwAiwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure gives the velocity \( u' \) of the particle relative to frame \( S' \) for a range of values for \( v \). The vertical axis scale is set by \( u'_a = 0.800c \). What value will \( u' \) have if \( v \rightarrow c \)?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D.... | C | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
0.042724609375,
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0.0029449462890625,
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0.000732421875,
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0.00135040283203125,
-0.00836181640625,
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0.0028839111328125,
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598 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAG2AcADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure gives their temporal separation \( \Delta t \) according to the \( S \) observer as a function of \( \Delta x' \) for a range of \( \Delta x' \) values. The vertical axis scale is set by \( \Delta t_a = 6.00\,\mu\text{s} \). What is \( \Delta t' \)?Please directly answer the question and provide the correct OPTI... | C | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.0289306640625,
-0.004150390625,
0.0021514892578125,
-0.011474609375,
-0.0186767578125,
0.0201416015625,
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0.00003981590270996094,
-0.0322265625,
0.01080322265625,
-0.039306640625,
0.04296875,
-0.01385498046875,
-0.00274658203125,
-0.0025482177734375,
0.01055908203125... |
599 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAMzA3YDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure gives \( \Delta t \) versus speed parameter \( eta \) for a range of values for \( eta \). The vertical axis scale is set by \( \Delta t_a = 14.0\,\text{s} \). What is interval \( \Delta t \) if \( v = 0.98c \)?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OP... | C | Modern Physics | Relativity | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.040771484375,
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0.0038299560546875,
0.01177978515625,
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0.03173828125,
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0.0238037109375,
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-0.0159912109375,
0.01104736328125,
0.01324462890625,
-0.01... |
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