Quantum Physics & Nuclear Decay

Photons and the photoelectric effect

Electromagnetic radiation is emitted and absorbed in quanta called photons, each of energy:

$$E = hf = \dfrac{hc}{\lambda}$$

where $h = 6.63\times10^{-34}\ \text{J s}$. In the photoelectric effect, photons eject electrons from a metal surface. Einstein's equation:

$$hf = \Phi + \tfrac{1}{2}mv_{max}^2$$

where $\Phi$ is the work function (minimum energy to release an electron). Key observations: emission is instantaneous; there is a threshold frequency below which no electrons are emitted regardless of intensity; the maximum kinetic energy depends on frequency, not intensity. This shows light behaves as particles.

A graph of maximum kinetic energy against frequency is a straight line of gradient $h$, intercepting the frequency axis at the threshold frequency $f_0$ and the energy axis at $-\Phi$.