Compton Scattering - AP Physics 2

1. Gamma rays of wavelength $2.0\times10^{-12}\,\text{m}$ scatter from electrons at rest; at $90^\circ$ the measured wavelength increases to $2.4\times10^{-12}\,\text{m}$. The wavelength increase occurs because the photon
   Answer: loses momentum in a collision and the electron gains recoil momentum. 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.
2. A beam of $\gamma$ photons is directed at electrons initially at rest. For photons scattered at the same angle, experiments show the scattered wavelength is always larger than the incident wavelength. The wavelength increase after scattering supports which inference about the interaction?
   Answer: The photon transfers momentum to the electron, reducing the photon's energy This question tests understanding of Compton scattering. The consistent wavelength increase for photons scattered at the same angle demonstrates that photons transfer momentum to electrons during collision. As particles with momentum p = h/λ, photons lose energy when they transfer momentum to the initially stationary electrons. This energy loss manifests as increased wavelength (E = hc/λ), while the electrons recoil with the transferred momentum and kinetic energy. Choice D incorrectly suggests the photon gains energy from the electron, which would decrease wavelength, contradicting observations. The key principle is that momentum transfer from photon to electron always reduces photon energy, increasing its wavelength.
3. X-ray photons scatter from electrons in graphite. The incident wavelength is $0.050\ \text{nm}$; at $180^\circ$ backscatter the wavelength becomes $0.0549\ \text{nm}$. Which conclusion about light is supported by this wavelength change?
   Answer: The photon behaves as a particle that transfers momentum to the electron. 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.
4. 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?
   Answer: Light behaves as particles with momentum, exchanging momentum with electrons. 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.
5. In a Compton scattering lab, $0.071\ \text{nm}$ X-rays strike nearly free electrons. A detector at $60^\circ$ measures scattered X-rays with wavelength $0.073\ \text{nm}$. Which conclusion about light is supported by the wavelength increase after scattering?
   Answer: The photon transfers momentum to an electron in a collision-like interaction. This problem tests understanding of Compton scattering. When X-rays scatter from electrons, the photon behaves as a particle with momentum p = h/λ, transferring some momentum to the electron through a collision-like interaction. The wavelength increase from 0.071 nm to 0.073 nm occurs because the photon loses energy and momentum to the electron, resulting in a longer wavelength (since E = hc/λ). This momentum transfer is exactly what we'd expect from a particle collision, supporting the particle nature of light. Choice B incorrectly suggests complete absorption and re-emission, which would be a different process (like fluorescence) with different wavelength characteristics. The key strategy is that momentum exchange reveals particle-like behavior of light.
6. A gamma-ray photon scatters from a nearly free electron, and the scattered photon has a longer wavelength than the incident photon. This supports the inference that the photon
   Answer: carries momentum and transfers some of it to the electron This question tests understanding of Compton scattering. The observation that scattered gamma rays have longer wavelengths than incident gamma rays supports the inference that photons carry momentum and transfer some of it to electrons. During the scattering event, conservation of momentum requires the initially stationary electron to recoil, taking some momentum from the photon, which results in the photon having lower momentum and thus longer wavelength. Choice D incorrectly claims complete absorption, but Compton scattering specifically involves inelastic scattering where the photon continues with reduced energy. The wavelength increase directly demonstrates momentum transfer from photon to electron.
7. An X-ray photon scatters from a stationary electron, and the detected wavelength is larger than the incident wavelength. Which conclusion about light is supported by this result?
   Answer: Light behaves as particles carrying momentum that can be transferred This question tests understanding of Compton scattering. The observation that scattered X-rays have larger wavelengths than incident X-rays provides direct evidence that light behaves as particles carrying momentum. During scattering, the photon transfers some of its momentum to the initially stationary electron, causing the photon's energy and frequency to decrease while its wavelength increases. Choice C incorrectly assumes complete absorption is necessary for scattering, when in fact Compton scattering involves partial momentum transfer without absorption. The wavelength shift in Compton scattering demonstrates that photons carry momentum that can be exchanged with matter.
8. An X-ray beam with initial wavelength $\lambda$ scatters from electrons at rest. For one detector at $30^\circ$, the scattered wavelength is $\lambda+\Delta\lambda$ (a measured increase). Which conclusion about light is supported by the observation?
   Answer: Photons carry momentum and transfer some to electrons during scattering. 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.
9. In a Compton setup, photons scatter from electrons and emerge with increased wavelength compared with the incident beam. Which conclusion about light is supported by this observation?
   Answer: Light consists of photons that carry momentum transferable to electrons This question tests understanding of Compton scattering. The observation that photons emerge with increased wavelength after scattering from electrons supports the conclusion that light consists of photons carrying momentum transferable to electrons. During scattering, the photon transfers some of its momentum to the initially stationary electron, causing the photon's wavelength to increase as its momentum decreases according to λ = h/p. Choice A incorrectly attributes wavelength changes only to wave interference, missing the particle-like momentum exchange central to Compton scattering. The systematic wavelength increase demonstrates that electromagnetic radiation exhibits particle properties with quantized momentum.
10. Gamma rays of wavelength $2.00\ \text{pm}$ scatter from electrons; at $60^\circ$ the wavelength becomes $2.49\ \text{pm}$. The wavelength increase occurs because the photon
    Answer: transfers momentum to the electron, reducing its own momentum This question tests understanding of Compton scattering. The gamma ray's wavelength increase from 2.00 pm to 2.49 pm at 60° scattering angle occurs because the photon transfers momentum to the electron during their collision. When the photon gives up momentum to make the electron recoil, the photon's own momentum decreases (p = h/λ), which means its wavelength must increase. Choice B incorrectly suggests photons slow down in air, but photons always travel at speed c in any medium where they propagate. Remember that momentum transfer during scattering reveals the particle-like behavior of electromagnetic radiation.
11. X-rays of wavelength $0.071\ \text{nm}$ scatter from electrons; a detector at $120^\circ$ measures $0.0759\ \text{nm}$. Which conclusion about light is supported by the wavelength change?
    Answer: The photon transfers momentum to the electron during scattering This question tests understanding of Compton scattering. The X-ray wavelength increase from 0.071 nm to 0.0759 nm at 120° scattering angle occurs because the photon transfers momentum to the electron during scattering. This momentum transfer is angle-dependent, with larger scattering angles typically producing larger wavelength shifts as more momentum is transferred to the electron. Choice A incorrectly suggests absorption and re-emission, which would not produce the systematic angle-dependent wavelength shifts observed in Compton scattering. The key principle is that photon-electron momentum exchange produces predictable wavelength changes based on scattering geometry.
12. X‑rays of wavelength $0.060\,\text{nm}$ 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 ____.
    Answer: energy decreases as it transfers momentum to the electron 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.
13. Gamma rays of wavelength $2.0\times10^{-12}\,\text{m}$ scatter from electrons initially at rest. At a fixed angle, the scattered wavelength is larger by $\Delta\lambda=4.9\times10^{-13}\,\text{m}$. The recoiling electrons are detected. The wavelength increase after scattering occurs because the photon must ____.
    Answer: lose energy while giving momentum to the electron in an elastic-like collision This question tests understanding of Compton scattering. In Compton scattering, gamma rays collide with electrons initially at rest, behaving as particles with momentum p = h/λ. The photon transfers some momentum to the electron during the collision, causing the photon to lose energy (E = hc/λ) and thus increase in wavelength by Δλ = 4.9×10⁻¹³ m. The electron recoils with the transferred momentum, and both energy and momentum are conserved in this elastic-like collision. Choice C incorrectly suggests full absorption and re-emission, which would be photoelectric effect, not Compton scattering where the photon continues with reduced energy. Remember that in Compton scattering, the photon always continues after collision with increased wavelength due to momentum transfer.
14. A $0.040\ \text{nm}$ X-ray scatters from an electron and is measured at $0.041\ \text{nm}$. Which statement best accounts for the observed wavelength increase?
    Answer: The photon loses momentum to the electron during a collision 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.
15. An X-ray beam scatters from electrons, and the scattered wavelength is observed to increase with scattering angle. Which conclusion about light is supported by this trend?
    Answer: Photons exchange momentum with electrons in angle-dependent collisions This question tests understanding of Compton scattering. The observation that scattered wavelength increases with scattering angle demonstrates that photons exchange momentum with electrons in angle-dependent collisions. Larger scattering angles correspond to more head-on collisions where greater momentum is transferred to the electron, resulting in larger wavelength increases for the scattered photon. Choice B incorrectly attributes wavelength changes solely to wave diffraction, missing the crucial role of momentum conservation in particle-like collisions. The angle dependence of wavelength shift provides strong evidence for the particle nature of light with quantized momentum.
16. In Compton scattering, an incident photon emerges at a larger wavelength than it had initially. Which conclusion about light is supported by this observation?
    Answer: Light has momentum and can recoil from electrons like particles This question tests understanding of Compton scattering. The emergence of photons at larger wavelengths after scattering demonstrates that light has momentum and can recoil from electrons like particles in collisions. When a photon collides with an electron, momentum conservation requires the photon to transfer some momentum to the electron, reducing the photon's own momentum and thus increasing its wavelength. Choice D incorrectly claims light carries no momentum, contradicting the fundamental relationship p = E/c = h/λ for photons. The wavelength increase in Compton scattering provides conclusive evidence for the particle-like momentum of light.
17. In an experiment, monochromatic gamma rays scatter from electrons at rest. The scattered wavelength is longer than the incident wavelength, and the electron is observed to recoil. Which conclusion about light is supported by these observations?
    Answer: Light transfers momentum to matter, consistent with particle-like photons. This problem involves Compton scattering. The observation of both a longer scattered wavelength and a recoiling electron provides direct evidence that light transfers momentum to matter, consistent with particle-like photons. The photon collides with the electron, transferring some of its momentum and energy, which causes the electron to recoil and the photon to have a longer wavelength (lower energy). These observations cannot be explained by pure wave behavior alone. Choice B incorrectly claims light is only a wave, which cannot explain the momentum transfer to the recoiling electron. Momentum exchange reveals particle-like behavior of light.
18. X-rays of wavelength $\lambda$ scatter from electrons initially at rest. A student finds $\Delta\lambda$ depends on scattering angle but not on the target material. Which conclusion about light is supported by this wavelength change behavior?
    Answer: The shift comes from photon–electron collisions, set by momentum conservation. This question examines Compton scattering. The wavelength shift depends only on scattering angle and not on target material because it results from photon-electron collisions governed by momentum conservation. The shift Δλ = λc(1 - cos θ) depends only on the scattering angle θ and the Compton wavelength λc = h/(mec), which involves only fundamental constants and electron mass. This material-independence proves the interaction is between individual photons and electrons, not a bulk material property. Choice A incorrectly suggests material-dependent refraction, which would vary with different targets. Momentum exchange reveals particle-like behavior of light.
19. In a Compton experiment, $0.050\ \text{nm}$ X-rays scatter from nearly free electrons and are detected at $90^\circ$ with wavelength $0.0524\ \text{nm}$. Which conclusion about light is supported by the wavelength increase?
    Answer: Light transfers momentum as particles in collisions with electrons 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.
20. Gamma-ray photons scatter from electrons at rest. A detector at $180^\circ$ measures a larger wavelength than the incident wavelength (increase after scattering). The wavelength increase occurs because the photon
    Answer: transfers momentum to the electron, reducing the photon's momentum. This question tests understanding of Compton scattering. At 180° (backscattering), the gamma-ray wavelength increases because the photon transfers momentum to the electron, reducing the photon's momentum. Maximum momentum transfer occurs at 180°, producing the largest possible wavelength shift for a given incident wavelength. Choice A incorrectly states the photon gains momentum from the electron, but the initially stationary electron cannot give momentum to the photon. The strategy is to recognize that larger scattering angles mean greater momentum transfer and larger wavelength increases.

Start this quiz