# 17.2.2 Photoelectric Equation

The electrons in the metal are bound to the metallic lattice, so work must be done in order to liberate them. Some of them are bound less loosely than others, so the amount of work required differs among them.

The least tightly bound electrons (those nearest to the metal surface) are the ones which require the least amount of work to break free from the metal lattice. This minimum work is called the work function F. Each type of metal has its own work function. For example, the work function for sodium, aluminium and gold are about 2.4 eV, 4.1 eV and 5.1 eV respectively.

Ok. We are now ready to relook the photoelectric effect through the new lens provided by the photon model.

So a beam of light is shone at a piece of metal. What do you see? We used to see a light wave crashing into the metal. Now we see discrete light energy packets raining down on the metal. It is like trying to rescue the imprisoned electrons by throwing energy balls at them.

If an electron is lucky enough to be “hit” by a photon, it can absorb the energy of the photon (hf). After using part of the energy to break free from the metal lattice (W), it escapes with the balance of the energy as its kinetic energy (KE). This energy transfer can be represented by the equation $\displaystyle KE=hf-W$

This explains why photoelectrons are emitted with a range of KE. Because the amount of required work W is different for each electron (depending on how tightly it is bound to the metal lattice). But there is a limit to the amount of KE the photoelectron can have. Since the minimum work required is F, the maximum KE must be $\displaystyle K{{E}_{{\max }}}=hf-\Phi$

Comics

Photon Bomb