Compton Scattering

When a photon collides with an electron, it bounces off like a billiard ball — losing some energy and gaining wavelength. The bigger the bounce angle, the more its wavelength stretches, and that wavelength shift depends only on the scattering angle, not on the photon's original energy or anything else about the collision. This was one of the clearest proofs that light travels in particle-like packets that carry momentum.

Δλ = (h / mₑc) · (1 − cos θ)

• Δλ — wavelength shift (m): how much longer the photon's wavelength becomes after scattering
• h / mₑc — Compton wavelength (m): a fixed constant equal to 2.43 picometers, set by the electron's mass
• θ — scattering angle (°): the angle between the photon's incoming and outgoing directions

A photon scatters straight off an electron at a 90 degree angle. How much does its wavelength shift?

• θ = 90°
• h / mₑc = 2.43 pm

1. Δλ = (h / mₑc) · (1 − cos θ)
2. Δλ = 2.43 pm · (1 − cos 90°) = 2.43 pm · 1

Δλ = 2.43 pm

Now the photon bounces straight backward, at a 180 degree angle. What is the wavelength shift?

• 4.86 pm
• 2.43 pm
• 1.22 pm

At which scattering angle does the photon's wavelength shift become zero?

• 180°
• 90°
• 0°