Photon Momentum and the Compton Scattering Wavelength Shift

All flashcards

How are photon energy and frequency related?

Photon energy is $E_f=hf$, where $h$ is Planck’s constant and $f$ is frequency.

What is the momentum magnitude of a photon?

$p_f=E_f/c=h/λ$, even though a photon has zero rest mass.

What is the Compton shift?

The difference between scattered and incident wavelengths: $Δλ=λ'-λ$.

What is the electron Compton wavelength?

$λ_c=h/(m_0c)$; for an electron, it is approximately $2.43\,\text{pm}$.

Why can Compton scattering produce an unshifted peak?

Scattering from tightly bound electrons or effectively from an entire atom can produce an extremely small, unresolved shift.

Quiz questions

1. In the classical wave account described for X-rays scattered by atoms, what is predicted about the scattered wavelength?Answer: It retains the incident wavelength.
2. According to the Compton relation, what is the wavelength shift at a scattering angle of $0°$?Answer: Zero; the incident and scattered wavelengths coincide.
3. Which quantities are conserved in the photon–electron collision model?Answer: Total relativistic energy and vector momentum.
4. Which expression gives the Compton wavelength shift for an electron initially at rest?Answer: $Δλ=\frac{h}{m_0c}(1-\cos θ)$
5. At what scattering angle is the Compton shift greatest, and what is its value for an electron?Answer: At $180°$; the maximum is $4.86\,\text{pm}$.