The Photoelectric Effect

Shine light on a metal and electrons can be ejected — but classical wave theory gets the details wrong. Einstein explained it (1905) by treating light as discrete photons of energy $E = h\nu$. An electron absorbs one photon; it needs energy $\phi$ (the work function) to escape the surface, and keeps the rest as kinetic energy:

$K_{\max} = h\nu - \phi.$

Two predictions that classical physics can't make, and experiment confirms: (1) below a threshold frequency ($h\nu < \phi$) no electrons are emitted no matter how bright the light, and (2) the maximum kinetic energy grows linearly with frequency, with slope $h$. This linear relationship was a decisive early piece of evidence for energy quantization.

Try it

This is a numerical exercise — return a number. A $3.0\,\text{eV}$ photon hits a metal whose work function is $2.0\,\text{eV}$. What is the maximum kinetic energy (in eV) of the ejected electron?

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