AP Physics 2 Quiz: Compton Scattering
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Compton ScatteringQuestion 1 of 20

In Compton scattering, an incident photon of wavelength λ\lambda scatters from an electron and emerges with wavelength λ′>λ\lambda'>\lambda. Which conclusion about light is supported by observing λ′>λ\lambda'>\lambda?

Photons carry momentum p=h/λp=h/\lambda and can recoil electrons during scattering.
Only diffraction effects in the material change the wavelength without energy transfer.
Electrons must absorb photons entirely, so scattering cannot involve momentum exchange.
The speed of light in vacuum decreases during scattering, causing the wavelength increase.
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AP Physics 2 Quiz

AP Physics 2 Quiz: Compton Scattering

Practice Compton Scattering in AP Physics 2 with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Compton Scattering, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Physics 2.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

In Compton scattering, an incident photon of wavelength λ\lambda scatters from an electron and emerges with wavelength λ′>λ\lambda'>\lambda. Which conclusion about light is supported by observing λ′>λ\lambda'>\lambda?

  1. Photons carry momentum p=h/λp=h/\lambda and can recoil electrons during scattering. (correct answer)
  2. Only diffraction effects in the material change the wavelength without energy transfer.
  3. Electrons must absorb photons entirely, so scattering cannot involve momentum exchange.
  4. The speed of light in vacuum decreases during scattering, causing the wavelength increase.

Explanation: This problem involves Compton scattering. The observation that λ' > λ indicates the photon lost energy during scattering, which occurs when the photon transfers momentum to the electron. Photons carry momentum p = h/λ, and during collision with electrons, momentum conservation requires the electron to recoil, taking some of the photon's initial momentum. Choice C incorrectly assumes complete absorption, but the presence of a scattered photon disproves this. The key principle is that momentum exchange between photons and electrons demonstrates light's particle nature.

Question 2

In Compton scattering, λ\lambda increases after a photon scatters from an electron. A student claims the change is due to the photon giving some of its momentum to the electron. Which statement is consistent with this claim and the measured wavelength increase?

  1. The scattered photon has smaller momentum magnitude than the incident photon (correct answer)
  2. The scattered photon has larger momentum magnitude than the incident photon
  3. The photon momentum is unchanged because only interference can change wavelength
  4. The photon momentum becomes zero because the electron absorbs it completely

Explanation: This question tests understanding of Compton scattering. Since photon momentum is p = h/λ, when wavelength λ increases after scattering, the momentum magnitude must decrease (they are inversely proportional). This occurs because the photon transfers some of its initial momentum to the electron during the collision. The electron recoils with this transferred momentum, while the photon continues with reduced momentum and energy, manifesting as the increased wavelength. Choice B incorrectly claims momentum increases with wavelength, violating the fundamental relationship p = h/λ. The strategy is to apply the momentum-wavelength relationship: larger wavelength always means smaller momentum for photons.

Question 3

X‑rays of wavelength 0.060 nm0.060\,\text{nm} scatter from electrons in a target. At a fixed scattering angle, detectors show a longer scattered wavelength than the incident wavelength, and recoil electrons are observed. The wavelength increase after scattering occurs because the photon's  .

  1. energy increases while its momentum decreases in the collision
  2. energy decreases as it transfers momentum to the electron (correct answer)
  3. frequency stays constant while its speed decreases in the target
  4. energy is unchanged because the electron only redirects the wavefront

Explanation: This question tests understanding of Compton scattering. The wavelength increase from 0.060 nm to a longer value indicates the photon's energy decreases during scattering, since E = hc/λ. This energy decrease occurs because the photon transfers momentum to the electron in a particle-like collision. The electron recoils with kinetic energy equal to the photon's lost energy, ensuring energy conservation. Both energy and momentum are transferred from photon to electron during the collision. Choice D incorrectly claims energy is unchanged, contradicting the observed wavelength increase which directly indicates energy loss. Remember that in Compton scattering, wavelength increase always means the photon loses energy by transferring momentum to the electron.

Question 4

Gamma rays of wavelength 3.0×10−12 m3.0\times10^{-12}\ \text{m} scatter from electrons at rest. At 90∘90^\circ, the scattered wavelength is larger by 2.4×10−12 m2.4\times10^{-12}\ \text{m}. The wavelength increase occurs because the photon

  1. is absorbed completely, and the electron later emits a new lower-energy photon.
  2. interferes with itself, producing an apparent shift without energy transfer.
  3. exchanges energy and momentum with an electron as a particle-like collision. (correct answer)
  4. slows down in the material so its wavelength becomes longer after scattering.

Explanation: This problem involves Compton scattering. The gamma ray photon collides with the electron like a billiard ball, exchanging both energy and momentum in a particle-like collision. The wavelength increase of 2.4×10⁻¹² m at 90° scattering angle occurs because the photon transfers momentum to the initially stationary electron, losing energy in the process. Since photon energy E = hc/λ, lower energy means longer wavelength. Choice D incorrectly describes complete absorption followed by emission, which would be a two-step process rather than the single scattering event observed. Momentum exchange reveals particle-like behavior of light.

Question 5

An X-ray beam scatters from electrons initially at rest. For 30∘30^\circ scattering, Δλ=0.48 pm\Delta\lambda=0.48\ \text{pm}; for 120∘120^\circ, Δλ=4.0 pm\Delta\lambda=4.0\ \text{pm}. Which conclusion about light is supported by the larger wavelength increase at larger angles?

  1. The wavelength shift is caused only by diffraction, which is stronger at larger angles.
  2. The photon keeps the same momentum, and only its direction changes with angle.
  3. The electron absorbs the photon completely more often at larger scattering angles.
  4. The photon's momentum changes more for larger deflection angles, like a collision. (correct answer)

Explanation: This question examines Compton scattering. The wavelength shift increases from 0.48 pm at 30° to 4.0 pm at 120° because larger scattering angles require greater momentum transfer between photon and electron. In a particle-like collision, a photon deflected through a larger angle must exchange more momentum with the electron, similar to how a billiard ball changes momentum more when deflected at larger angles. This angle-dependent momentum transfer directly supports the particle nature of light. Choice C incorrectly attributes the shift to diffraction, which is a wave phenomenon that doesn't explain the specific angle dependence observed. Momentum exchange reveals particle-like behavior of light.

Question 6

In Compton scattering, 0.040 nm0.040\,\text{nm} X-rays strike electrons initially at rest. Photons detected at 90∘90^\circ have wavelength 0.0424 nm0.0424\,\text{nm} (increased after scattering). Which conclusion about light is supported by the data?

  1. The photon's speed changes in vacuum, producing a longer wavelength.
  2. The shift occurs because waves diffract around electrons with no momentum exchange.
  3. Photons carry momentum and can collide with electrons, causing recoil. (correct answer)
  4. Electrons absorb all photon energy, so any scattered photon is newly created.

Explanation: This question tests understanding of Compton scattering. The X-ray wavelength increase from 0.040 nm to 0.0424 nm at 90° scattering supports the conclusion that photons carry momentum and can collide with electrons, causing recoil. The 90° geometry produces a specific wavelength shift Δλ = h/(mc)(1-cos90°) = h/(mc), demonstrating quantitative momentum conservation. Choice A incorrectly claims no momentum exchange occurs in wave diffraction, but diffraction doesn't change wavelength. The key insight is that measurable wavelength shifts prove photon-electron collisions follow particle mechanics with momentum conservation.

Question 7

A beam of 0.100 nm0.100\ \text{nm} X-rays scatters from electrons initially at rest. A detector at 45∘45^\circ measures 0.101 nm0.101\ \text{nm} after scattering. The wavelength increase occurs because the scattered photon has

  1. the same momentum magnitude, with the change explained only by interference.
  2. a smaller momentum magnitude after transferring momentum to the electron. (correct answer)
  3. zero momentum because it is briefly absorbed before being re-emitted.
  4. a larger momentum magnitude after gaining momentum from the electron.

Explanation: This question tests Compton scattering. The X-ray photon transfers momentum to the electron during scattering, causing the photon's momentum magnitude to decrease. Since photon momentum p = h/λ, when wavelength increases from 0.100 nm to 0.101 nm, the momentum must decrease proportionally. This momentum decrease occurs because some of the photon's initial momentum is transferred to the electron, which recoils after the collision. Choice C incorrectly claims the momentum magnitude stays the same, which would violate conservation of momentum since the electron gains momentum. Momentum exchange reveals particle-like behavior of light.

Question 8

X-ray photons scatter from electrons at rest; the detected scattered wavelength is greater than the incident wavelength (increase after scattering). Which conclusion about light is supported by this wavelength change?

  1. The shift is explained entirely by wave interference with no collisions.
  2. Light carries momentum as photons, so scattering transfers momentum to electrons. (correct answer)
  3. Light transfers only energy, so electron recoil is impossible.
  4. Electrons must capture photons, then emit longer-wavelength photons later.

Explanation: This question tests understanding of Compton scattering. The observed wavelength increase after X-rays scatter from electrons supports the conclusion that light carries momentum as photons, so scattering transfers momentum to electrons. This momentum transfer causes the photon to lose energy (longer wavelength) while the electron gains kinetic energy, satisfying conservation laws. Choice A incorrectly denies photon momentum, contradicting the experimental evidence of wavelength shifts. The key strategy is recognizing that wavelength changes in scattering experiments provide direct evidence for light's particle-like momentum.

Question 9

A beam of gamma rays scatters from electrons initially at rest. The scattered photons are measured to have a longer wavelength than the incident photons (increase after scattering). The wavelength increase occurs because

  1. the photon's electric field oscillates slower after passing the electron.
  2. interference between incident and scattered waves shifts the wavelength.
  3. the photon loses energy in a particle-like collision, so its momentum decreases. (correct answer)
  4. the electron emits a new photon after absorbing the original photon completely.

Explanation: This question tests understanding of Compton scattering. Gamma rays show increased wavelength after scattering because the photon loses energy in a particle-like collision, so its momentum decreases. Since E = pc for photons and p = h/λ, decreased momentum means increased wavelength. Choice D incorrectly suggests interference causes the shift, but interference between waves cannot change the wavelength of scattered photons—only their intensity distribution. The fundamental concept is that energy-momentum conservation in photon-electron collisions produces predictable wavelength shifts.

Question 10

An experiment observes that X-ray wavelength increases after scattering from electrons at rest, and the increase is larger at larger scattering angles. Which conclusion about light is supported by these observations?

  1. Light behaves as particles with momentum, exchanging momentum with electrons. (correct answer)
  2. Light is only a wave, and the angle dependence is due to interference only.
  3. Electrons fully absorb photons, and the angle dependence is from re-emission.
  4. The wavelength increase proves the photon's charge changes with angle.

Explanation: This question tests understanding of Compton scattering. The observation that wavelength increase depends on scattering angle (larger angles produce larger shifts) supports the conclusion that light behaves as particles with momentum, exchanging momentum with electrons. The angle dependence follows Δλ = (h/mc)(1-cosθ), which derives from relativistic momentum conservation in particle collisions. Choice B incorrectly attributes the angle dependence to interference, but interference patterns don't change individual photon wavelengths. The principle is that angle-dependent wavelength shifts uniquely demonstrate particle-like momentum exchange in light-matter interactions.

Question 11

X-ray photons scatter from electrons in graphite. The incident wavelength is 0.050 nm0.050\ \text{nm}; at 180∘180^\circ backscatter the wavelength becomes 0.0549 nm0.0549\ \text{nm}. Which conclusion about light is supported by this wavelength change?

  1. The photon's energy stays constant, and only its direction changes during scattering.
  2. The photon is absorbed and the electron emits a longer-wavelength photon after thermalization.
  3. The photon behaves as a particle that transfers momentum to the electron. (correct answer)
  4. The wavelength increase is purely a standing-wave effect that requires no momentum transfer.

Explanation: This problem demonstrates Compton scattering. The X-ray photon behaves as a particle that transfers momentum to the electron during the collision. The wavelength increase from 0.050 nm to 0.0549 nm at 180° backscatter represents the maximum possible wavelength shift, occurring when the photon reverses direction and transfers maximum momentum to the electron. This momentum transfer causes the photon to lose energy, resulting in a longer wavelength since E = hc/λ. Choice A incorrectly suggests no momentum transfer, which would mean no wavelength change could occur. Momentum exchange reveals particle-like behavior of light.

Question 12

An X-ray photon scatters from a free electron, and the scattered wavelength is longer than the incident wavelength. The electron is detected moving afterward. The wavelength increase occurs because the photon

  1. is refracted by the electron, which changes wavelength without changing photon momentum.
  2. is absorbed and then re-emitted later, so scattering is not a single interaction.
  3. transfers energy and momentum to the electron in a particle-like collision. (correct answer)
  4. constructively interferes with itself at the detector, producing an apparent shift.

Explanation: This problem demonstrates Compton scattering. The photon transfers energy and momentum to the electron in a particle-like collision, causing both the wavelength increase and the electron's motion. The simultaneous observation of a longer wavelength (lower energy photon) and a moving electron proves that momentum and energy are conserved in a single collision event. This behavior matches exactly what we'd expect from two particles colliding and exchanging momentum. Choice B incorrectly describes absorption and re-emission as separate events, which would show different timing and wouldn't conserve momentum in a single interaction. Momentum exchange reveals particle-like behavior of light.

Question 13

Gamma-ray photons scatter from electrons initially at rest. The measured wavelength shift is Δλ=λC(1−cos⁡θ)\Delta\lambda=\lambda_C(1-\cos\theta), increasing with θ\theta. Which conclusion about light is supported by this relationship?

  1. Photons carry momentum and exchange it with electrons during scattering. (correct answer)
  2. Electrons must absorb photons completely, so the scattered photon is newly created.
  3. Scattering is explained entirely by wave superposition, not by momentum exchange.
  4. Photons gain energy from electrons, so larger angles always produce shorter wavelengths.

Explanation: This question involves Compton scattering. The measured relationship Δλ = λc(1 - cos θ) directly supports that photons carry momentum and exchange it with electrons during scattering. This formula, derived from momentum and energy conservation in particle collisions, shows the wavelength shift increases with scattering angle θ because larger angles require greater momentum transfer. The (1 - cos θ) factor reaches its maximum at θ = 180°, corresponding to maximum momentum transfer in backscattering. Choice D incorrectly claims photons gain energy from electrons, which would decrease wavelength, opposite to what's observed. Momentum exchange reveals particle-like behavior of light.

Question 14

In a Compton-scattering setup, 0.050 nm0.050\,\text{nm} X-rays strike electrons initially at rest. A detector measures scattered photons at 60∘60^\circ with wavelength 0.053 nm0.053\,\text{nm} (an increase after scattering). Which conclusion about light is supported by this wavelength change?

  1. The wavelength shift is caused only by wave interference in the detector.
  2. Light transfers energy but not momentum, so only wavelength changes.
  3. The photon is completely absorbed and re-emitted with a longer wavelength.
  4. Light behaves as particles with momentum, transferring momentum to electrons. (correct answer)

Explanation: This question tests understanding of Compton scattering. When X-rays scatter from electrons at rest, the observed wavelength increase (from 0.050 nm to 0.053 nm) demonstrates that photons behave as particles carrying momentum. During the collision, the photon transfers some of its momentum to the electron, causing the electron to recoil and the photon to lose energy, which increases its wavelength. Choice A incorrectly claims light has no momentum, missing the particle nature that Compton scattering proves. The key insight is that momentum conservation between photon and electron particles explains the wavelength shift, confirming light's dual wave-particle nature.

Question 15

Gamma rays of wavelength 2.0×10−12 m2.0\times10^{-12}\,\text{m} scatter from electrons at rest; at 90∘90^\circ the measured wavelength increases to 2.4×10−12 m2.4\times10^{-12}\,\text{m}. The wavelength increase occurs because the photon

  1. interferes destructively with the incident wave, shifting its frequency.
  2. is absorbed entirely and then re-emitted after a time delay.
  3. loses momentum in a collision and the electron gains recoil momentum. (correct answer)
  4. diffracts around the electron, creating a longer effective path length.

Explanation: This question tests understanding of Compton scattering. The gamma ray's wavelength increases from 2.0×10⁻¹² m to 2.4×10⁻¹² m after scattering at 90°, which occurs because the photon loses momentum in a collision with the electron. In this particle-like interaction, momentum conservation requires the initially stationary electron to gain recoil momentum equal and opposite to the photon's momentum loss. Choice B incorrectly suggests diffraction causes the shift, but diffraction doesn't change wavelength—only scattering angle. The strategy is to recognize that wavelength increase always indicates momentum transfer from photon to electron.

Question 16

X-ray photons of wavelength 0.070 nm0.070\,\text{nm} scatter from electrons initially at rest. At 120∘120^\circ the scattered wavelength is 0.074 nm0.074\,\text{nm} (increased after scattering). The wavelength increase occurs because the photon's

  1. energy stays the same, but dispersion in air stretches its wavelength.
  2. momentum decreases as it transfers momentum to the recoiling electron. (correct answer)
  3. wavefronts interfere after scattering, producing a longer measured wavelength.
  4. electric field amplitude decreases, which increases wavelength automatically.

Explanation: This question tests understanding of Compton scattering. The X-ray wavelength increases from 0.070 nm to 0.074 nm when scattered at 120° because the photon's momentum decreases as it transfers momentum to the recoiling electron. Since photon momentum p = h/λ, a decrease in momentum directly causes an increase in wavelength. Choice C incorrectly attributes the shift to wave interference, but interference cannot change the wavelength of individual photons—only their intensity pattern. The key concept is that momentum exchange in particle-like collisions explains wavelength shifts in Compton scattering.

Question 17

An X-ray beam with initial wavelength λ\lambda scatters from electrons at rest. For one detector at 30∘30^\circ, the scattered wavelength is λ+Δλ\lambda+\Delta\lambda (a measured increase). Which conclusion about light is supported by the observation?

  1. Light is purely a wave, so scattering changes wavelength by interference alone.
  2. Electrons absorb photons completely, then emit longer-wavelength photons.
  3. Photons carry momentum and transfer some to electrons during scattering. (correct answer)
  4. Photons have zero momentum, so electron recoil is unrelated to the shift.

Explanation: This question tests understanding of Compton scattering. The observed wavelength increase (from λ to λ+Δλ) at 30° scattering angle demonstrates that photons carry momentum and transfer some to electrons during scattering. This momentum transfer causes the photon to lose energy (E = pc for photons), which manifests as increased wavelength since E = hc/λ. Choice B incorrectly assumes complete absorption followed by emission, but Compton scattering involves elastic collisions where the photon continues existing throughout. The principle to remember is that photon-electron collisions conserve both energy and momentum, proving light's particle nature.

Question 18

A 0.060 nm0.060\ \text{nm} X-ray photon scatters from a stationary electron; the scattered photon is measured at 0.062 nm0.062\ \text{nm}. The wavelength increase occurs because the photon

  1. slows down after scattering, making λ\lambda larger at constant frequency
  2. loses momentum to the electron, lowering its energy and frequency (correct answer)
  3. is absorbed and re-emitted with the same energy but different direction
  4. interferes with itself in the target, producing a longer wavelength

Explanation: This question tests understanding of Compton scattering. The X-ray wavelength increase from 0.060 nm to 0.062 nm occurs because the photon loses momentum to the electron, which lowers the photon's energy and frequency. Since E = hf and c = fλ, a decrease in frequency must correspond to an increase in wavelength while the photon continues to travel at speed c. Choice A incorrectly suggests photons slow down, but photon speed is always c in vacuum regardless of energy. The fundamental mechanism is momentum transfer: the photon gives up momentum to make the electron recoil, resulting in reduced photon energy and increased wavelength.

Question 19

A 0.040 nm0.040\ \text{nm} X-ray scatters from an electron and is measured at 0.041 nm0.041\ \text{nm}. Which statement best accounts for the observed wavelength increase?

  1. The photon's speed decreases after scattering, so λ\lambda increases
  2. Wave superposition in the target creates a longer wavelength photon
  3. The photon loses momentum to the electron during a collision (correct answer)
  4. The electron emits a new photon with higher energy than the original

Explanation: This question tests understanding of Compton scattering. The X-ray wavelength increase from 0.040 nm to 0.041 nm occurs because the photon loses momentum to the electron during their collision. Conservation of momentum requires that as the electron recoils with some momentum, the photon's momentum must decrease, which manifests as an increase in wavelength since λ = h/p. Choice B incorrectly claims the photon's speed decreases, but all photons travel at speed c regardless of their energy or wavelength. The fundamental principle is that momentum exchange between photons and electrons causes the observed wavelength shift.

Question 20

In a Compton experiment, 0.050 nm0.050\ \text{nm} X-rays scatter from nearly free electrons and are detected at 90∘90^\circ with wavelength 0.0524 nm0.0524\ \text{nm}. Which conclusion about light is supported by the wavelength increase?

  1. Light transfers momentum as particles in collisions with electrons (correct answer)
  2. Electrons absorb each photon completely and later re-emit it unchanged
  3. Light changes wavelength only due to wave interference in the detector
  4. Light has no momentum, so electrons recoil only from electric forces

Explanation: This question tests understanding of Compton scattering. When X-rays scatter from electrons, the observed wavelength increase from 0.050 nm to 0.0524 nm demonstrates that photons transfer momentum to electrons during collision-like interactions. This momentum transfer causes the photon to lose energy (E = hc/λ), resulting in a longer wavelength for the scattered photon while the electron recoils with the transferred momentum. Choice B incorrectly attributes the wavelength change to wave interference, missing the particle-like momentum exchange that is fundamental to Compton scattering. The key insight is that momentum conservation in photon-electron collisions reveals light's particle nature.