The photoelectric effect

What just happened?

The photoelectric effect is the ejection of electrons from a metal by incident light. Each photon gives all of its energy to a single electron.

Kinetic energy of the ejected electron:

— the photon energy $hf$ minus the work function $W$ (the minimum energy needed to tear an electron out of the metal). $h = 6{.}63\cdot10^{-34}\,\text{J·s}$ is Planck's constant.

Threshold frequency:

Below $f_0$ the photon has too little energy ($hf < W$) and no electron is ejected. Above it — $E_k$ grows linearly with frequency.

Why isn't intensity alone enough?

One photon = one electron. Higher intensity means more photons, so more ejected electrons — but each photon still carries the same energy $hf$. If that energy does not exceed $W$, then no matter how blinding the light, no current will flow.

Evidence for light quanta:

The existence of a sharp threshold $f_0$ and the linear dependence $E_k(f)$ were inexplicable for a classical wave. Only the photon — a portion (quantum) of light energy — explains the photoelectric effect. Einstein received the Nobel Prize for this explanation.

Why you need this for the exam:

$E_k = hf - W$ and $f_0 = W/h$ solve most photoelectric-effect problems. The trick: first check whether $hf > W$ (whether there are any electrons at all), then compute $E_k$ — and remember that intensity changes the number of electrons, not their energy.

Remember: what decides whether an electron is ejected is frequency, not intensity — $E_k = hf - W$, and the threshold is $f_0 = W/h$.