Playing Billiards with Photons
While the Photoelectric effect proves that photons act like particles when they are absorbed, Compton Scattering proves they act like particles when they collide.
In 1923, Arthur Compton fired high-energy X-rays at graphite. He found that the X-rays bouncing off the target had a slightly longer wavelength (lower energy) than the X-rays going in.
Conservation of Momentum
Compton realized that a photon was literally colliding with a stationary electron like a billiard ball.
- The photon hits the electron and transfers some of its energy and momentum to it.
- The electron goes flying off in one direction.
- The photon ricochets in another direction. Because it lost energy, its frequency drops and its wavelength increases.
This shift in wavelength only depends on the angle at which the photon scatters, not on the original energy of the photon.
The Formula
Where:
=
Shift in Wavelength (λ_final - λ_initial)=
Compton Wavelength of the electron (~2.426 pm)=
Scattering Angle of the photonExample Calculation
An X-ray photon ricochets off an electron at exactly $90^\circ$.
- Calculate Cosine: $\cos(90^\circ) = 0$.
- Calculate (1 - cos): $1 - 0 = 1$.
- Multiply by Compton Wavelength: $2.426 \times 10^{-12} , \text{m} \times 1 = 2.426 \times 10^{-12} , \text{m}$.
The scattered X-ray will have a wavelength that is exactly $0.002426 , \text{nm}$ longer than it was originally.