Compton Scattering

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AP Physics 2 › Compton Scattering

Questions 1 - 10
1

In Compton scattering, an incident photon emerges at a larger wavelength than it had initially. Which conclusion about light is supported by this observation?

Light has momentum and can recoil from electrons like particles

Electrons can only scatter light by absorbing it completely

Light’s wavelength changes only from interference between wavefronts

Light carries energy but no momentum, so electrons cannot recoil

Explanation

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.

2

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

transfers momentum to the electron, reducing its own momentum

diffracts around atoms, creating a longer apparent wavelength

slows down in air after scattering, increasing its wavelength

is fully absorbed by the electron, so no scattered photon should exist

Explanation

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.

3

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?

Electrons absorb each photon completely and later re-emit it unchanged

Light changes wavelength only due to wave interference in the detector

Light transfers momentum as particles in collisions with electrons

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.

4

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?

Electrons must absorb photons completely in every scattering event

Light behaves as a wave only, and interference increases the wavelength

Light has energy but cannot exchange momentum with matter

Light behaves as particles carrying momentum that can be transferred

Explanation

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.

5

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

is absorbed and re-emitted with the same energy but different direction

loses momentum to the electron, lowering its energy and frequency

slows down after scattering, making $\lambda$ larger at constant frequency

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.

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

carries momentum and transfers some of it to the electron

has no momentum, so the electron’s recoil must be unrelated to the photon

is completely absorbed, so any detected photon must be from another source

is a wave only, and the wavelength change comes from interference patterns

Explanation

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 beam scatters from electrons, and the scattered wavelength is observed to increase with scattering angle. Which conclusion about light is supported by this trend?

Electrons must absorb photons completely for scattering to occur

Photons exchange momentum with electrons in angle-dependent collisions

Photon momentum is zero, so angle cannot affect wavelength

Only wave diffraction determines the wavelength after scattering

Explanation

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.

8

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’s speed decreases after scattering, so $\lambda$ increases

The electron emits a new photon with higher energy than the original

Wave superposition in the target creates a longer wavelength photon

The photon loses momentum to the electron during a collision

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.

9

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 photon’s frequency stays the same, but its speed decreases

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 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.

10

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?

Electrons absorb photons completely, so any scattering is secondary emission

Light has energy but cannot exchange momentum with matter in collisions

Light consists of photons that carry momentum transferable to electrons

Light’s wavelength changes only because of interference between waves

Explanation

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.

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