Explain the photoelectric effect using the photon model, including threshold frequency, work function and maximum kinetic energy.

What this dot point is asking

You need to explain the photoelectric effect using the photon model and apply the photoelectric equation involving threshold frequency, work function and maximum kinetic energy.

What is observed

When light of high enough frequency hits a metal, electrons (photoelectrons) are emitted. Experiments show:

• There is a threshold frequency $f_0$: below it, no electrons are emitted no matter how intense or how long the light shines.
• Above $f_0$, electrons are emitted instantly, even at very low intensity.
• The maximum kinetic energy of the electrons depends on the light's frequency, not its intensity.
• Greater intensity (above threshold) means more electrons per second, but not more energetic ones.

Why the wave model fails

The wave model predicts that energy is spread continuously across the wavefront, so a dim light should take time to build up enough energy in an electron, and any frequency should eventually work given enough intensity. Both predictions are wrong: emission is instant above threshold and impossible below it, regardless of intensity. The wave model cannot explain a threshold frequency or instantaneous emission.

Einstein's photon explanation

To escape the metal, an electron must be given at least the work function $W$ - the minimum energy to free an electron from the surface. Any leftover photon energy becomes the electron's kinetic energy.

This explains every observation: below $f_0$ a single photon lacks the energy to free an electron (so no amount of intensity helps); above $f_0$ emission is instant (one photon, one electron); and higher frequency means more leftover energy.

Stopping voltage

The maximum kinetic energy can be measured with a stopping voltage $V_0$, the reverse voltage that just halts the most energetic electrons: $E_{k,\text{max}} = eV_0$. A graph of $E_{k,\text{max}}$ (or $V_0$) against frequency is a straight line of gradient $h$ and frequency-intercept $f_0$ - a classic way to measure Planck's constant.