A physicist repeats Compton's experiment using ultraviolet light (λ ≈ 100 nm) instead of X-rays, measuring the scattered wavelength at θ = 90°. How large is the wavelength shift?
AMuch larger than for X-rays, because UV photons have higher energy
BMuch smaller than for X-rays, because UV photons have lower momentum
CApproximately 2.4 pm — the same as for X-rays at the same angle, because the Compton shift depends only on scattering angle and fundamental constants
DZero, because UV light is not energetic enough to transfer momentum to an electron
The Compton formula Δλ = (h/m_e c)(1 − cos θ) contains no term for the incident wavelength — only the scattering angle θ and fundamental constants (h, m_e, c). At θ = 90°, Δλ = h/m_e c ≈ 2.4 pm regardless of whether you use soft X-rays, hard X-rays, or UV. The fractional shift Δλ/λ is much smaller for UV (λ ≈ 100 nm) than for hard X-rays (λ ≈ 0.1 nm), which is why the effect wasn't first detected with visible or UV light, but the absolute shift is the same.
Question 2 Multiple Choice
How did classical electromagnetic theory (Thomson scattering) predict the outcome of X-ray scattering off electrons, before Compton's experiment?
AThe scattered X-rays should have a shorter wavelength, as energy is transferred from photon to electron
BThe scattered X-rays should have the same wavelength as the incident X-rays — the driven electron re-radiates at the same frequency it was driven at
CThe scattered X-rays should show the same wavelength shift as Compton observed
DNo scattering should occur because classical electrons are too light to deflect X-rays
In Thomson scattering, the oscillating electric field of an X-ray forces the electron to oscillate at the same frequency. The accelerating electron then re-radiates electromagnetic waves at that same frequency — no wavelength change is predicted. This is why Compton's observation of a real, angle-dependent wavelength shift was so striking: it was completely inexplicable by classical wave theory and required treating the photon as a particle with momentum.
Question 3 True / False
The Compton wavelength shift at a given scattering angle is the same whether the incident photon is a soft X-ray or a hard X-ray.
TTrue
FFalse
Answer: True
The Compton formula Δλ = (h/m_e c)(1 − cos θ) is independent of the incident wavelength. The absolute shift depends only on the scattering angle and fundamental constants. This is one of the formula's most striking features, and it was confirmed by Compton's data across multiple X-ray energies. The fractional shift Δλ/λ does depend on the incident wavelength — which is why the effect is only observable with X-rays (λ ~ 0.1 nm) and not with visible light (λ ~ 500 nm).
Question 4 True / False
Compton scattering was primarily significant for confirming that light travels at the speed c in most inertial frames.
TTrue
FFalse
Answer: False
Compton scattering proved that photons carry momentum (p = h/λ) and interact as particles in elastic collisions — not anything about the speed of light. The speed of light was already firmly established. The revolutionary insight from Compton's experiment was photon momentum: Einstein had proposed p = h/λ, but the photoelectric effect couldn't test it (photons were absorbed, not scattered). Compton's experiment — where photons bounced off electrons at measurable angles with predictable momentum transfer — was the decisive test.
Question 5 Short Answer
Why couldn't the photoelectric effect alone prove that photons carry momentum, and what made Compton scattering the decisive evidence?
Think about your answer, then reveal below.
Model answer: In the photoelectric effect, photons are absorbed by electrons — the photon disappears. An absorbed particle transfers its energy, but there is no way to measure the momentum transfer independently of the energy, so the momentum hypothesis p = h/λ couldn't be directly tested. In Compton scattering, the photon bounces off the electron and continues in a new direction — it survives the collision. By measuring both the scattered photon's new wavelength and the electron's recoil angle, Compton could check that both energy and momentum were conserved according to relativistic mechanics, with p_photon = h/λ. The agreement between the formula and data at every angle confirmed photon momentum directly.
The key distinction is absorption vs. scattering. Scattering is a two-body collision with two measurable final states (scattered photon + recoiling electron), allowing independent tests of momentum conservation. This is what made Compton's experiment so compelling — the particle-collision model made specific, quantitative predictions about how the wavelength shift would vary with angle, and those predictions matched data precisely.