Compton Scattering
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AP Physics 2 › Compton Scattering
In Compton scattering, an incident photon of wavelength $\lambda$ scatters from an electron and emerges with wavelength $\lambda'>\lambda$. Which conclusion about light is supported by observing $\lambda'>\lambda$?
Electrons must absorb photons entirely, so scattering cannot involve momentum exchange.
The speed of light in vacuum decreases during scattering, causing the wavelength increase.
Only diffraction effects in the material change the wavelength without energy transfer.
Photons carry momentum $p=h/\lambda$ and can recoil electrons during scattering.
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.
In Compton scattering, $\lambda$ 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?
The scattered photon has larger momentum magnitude than the incident photon
The photon momentum is unchanged because only interference can change wavelength
The scattered photon has smaller momentum magnitude than the incident photon
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.
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 ____.
energy is unchanged because the electron only redirects the wavefront
energy decreases as it transfers momentum to the electron
frequency stays constant while its speed decreases in the target
energy increases while its momentum decreases in the collision
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.
A $0.060\ \text{nm}$ X-ray photon scatters from a stationary electron; the scattered photon is measured at $0.062\ \text{nm}$. The wavelength increase occurs because the photon
interferes with itself in the target, producing a longer wavelength
loses momentum to the electron, lowering its energy and frequency
slows down after scattering, making $\lambda$ larger at constant frequency
is absorbed and re-emitted with the same energy but different direction
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.
Gamma rays of wavelength $3.0\times10^{-12}\ \text{m}$ scatter from electrons at rest. At $90^\circ$, the scattered wavelength is larger by $2.4\times10^{-12}\ \text{m}$. The wavelength increase occurs because the photon
is absorbed completely, and the electron later emits a new lower-energy photon.
interferes with itself, producing an apparent shift without energy transfer.
slows down in the material so its wavelength becomes longer after scattering.
exchanges energy and momentum with an electron as a particle-like collision.
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.
An X-ray beam scatters from electrons initially at rest. For $30^\circ$ scattering, $\Delta\lambda=0.48\ \text{pm}$; for $120^\circ$, $\Delta\lambda=4.0\ \text{pm}$. Which conclusion about light is supported by the larger wavelength increase at larger angles?
The electron absorbs the photon completely more often at larger scattering angles.
The photon’s momentum changes more for larger deflection angles, like a collision.
The wavelength shift is caused only by diffraction, which is stronger at larger angles.
The photon keeps the same momentum, and only its direction changes with angle.
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.
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?
The wavelength increase is caused only by diffraction in the apparatus
The photon is absorbed and the electron later emits an identical photon
The photon’s frequency stays the same, but its speed decreases
The photon transfers momentum to the electron during scattering
Explanation
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.
In Compton scattering, $0.040,\text{nm}$ X-rays strike electrons initially at rest. Photons detected at $90^\circ$ have wavelength $0.0424,\text{nm}$ (increased after scattering). Which conclusion about light is supported by the data?
Electrons absorb all photon energy, so any scattered photon is newly created.
Photons carry momentum and can collide with electrons, causing recoil.
The photon’s speed changes in vacuum, producing a longer wavelength.
The shift occurs because waves diffract around electrons with no momentum exchange.
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.
A beam of $0.100\ \text{nm}$ X-rays scatters from electrons initially at rest. A detector at $45^\circ$ measures $0.101\ \text{nm}$ after scattering. The wavelength increase occurs because the scattered photon has
a smaller momentum magnitude after transferring momentum to the electron.
zero momentum because it is briefly absorbed before being re-emitted.
the same momentum magnitude, with the change explained only by interference.
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.
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?
The photon loses momentum to the electron during a collision
Wave superposition in the target creates a longer wavelength photon
The photon’s speed decreases after scattering, so $\lambda$ increases
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.