13.3 Einstein’s photoelectric effect equation

Conservation of energy and the photoelectric effect
Energy of each individual photon must be conserved. This energy:
1. Frees a single electron from the surface of the metal in a one-to-one interaction
2. Any remainder energy is transferred into KE pf photoelectron

Define work function
Minimum energy to free electron from a particular metal

Einstein’s photoelectric effect equation
Energy of a single photon = minimum energy required to free a single electron from the metal surface + maximum kinetic energy of emitted electron
Einstein's photoelectric effect equation

Why maximum kinetic energy?
Some electrons in surface of metal closer to +ve metal ions than others. Position affects how much energy required to free them. An electron that requires min amount of energy to free it (work function) would have the most energy left over from the incident photon. Only few emitted photoelectrons have this max KE

If photon strikes surface at threshold frequency
If incident frequency=ƒ₀ then only has enough energy to free a surface electron, with none left over to be transferred into KE
Eqn becomes hƒ₀=∅

A graph of KEmax against incident frequency
KE on y axis, f on x axis. Using y=mx+c, KEmax=hf-∅ ∴ gradient is Planck’s constant and y intercept is −work function