Topic 15.5 The Photoelectric Effect and Compton Scattering: apply the photoelectric equation and describe Compton scattering as evidence of the photon.

What this topic is asking

The College Board (Topics 15.5 and 15.6) want you to apply the photoelectric equation, $K_{max} = hf - \phi$, explain why the photoelectric effect proves the photon model, and describe Compton scattering as evidence that photons carry momentum.

The photoelectric effect

The photoelectric effect is the experiment that forced physics to accept photons. Classically, a bright enough light of any frequency should eventually shake electrons loose, but experiment shows the opposite: below a threshold frequency, no electrons are emitted however bright the light, while above it electrons are emitted instantly even for dim light. This makes sense only if light arrives as photons, each carrying energy $hf$: an electron is freed only if the single photon that hits it has enough energy ($hf \geq \phi$).

The photoelectric equation

The equation is energy conservation for a single photon-electron interaction: the photon's energy $hf$ pays the "exit fee" $\phi$ to free the electron, and the leftover becomes the electron's kinetic energy. Two predictions distinguish it sharply from the wave model. First, there is a hard threshold: below $f_0$, nothing happens at any intensity. Second, intensity changes count, not energy: brighter light means more photons, so more electrons, but each electron's energy still depends only on $hf$. These are the most-tested points.

Compton scattering: photons carry momentum

The photoelectric effect shows photons carry energy; Compton scattering shows they also carry momentum. When X-ray photons scatter off electrons, the scattered light comes out with a longer wavelength (lower energy), and the electron recoils, exactly as in a particle collision where momentum and energy are conserved. The photon behaves like a particle with momentum $p = \dfrac{h}{\lambda}$, transferring some to the electron. This is decisive: only a particle can collide and share momentum like this; a spread-out wave cannot. The strategic role of these topics is that they provide the experimental backbone of the photon model introduced in Topic 15.1: the photoelectric effect proves light delivers energy in quanta, and Compton scattering proves photons carry momentum. Together with interference (which shows the wave side), they complete the case for wave-particle duality and set up the quantised atomic energy levels of Topic 15.2.

Try this

Q1. State what happens to the number of ejected electrons and their maximum kinetic energy when the light's intensity is increased (frequency fixed). [2 points]

• Cue. More electrons are ejected, but their maximum kinetic energy is unchanged.

Q2. State what Compton scattering shows about photons. [1 point]

• Cue. That photons carry momentum (they collide with electrons like particles).