Problem 6.

A metal surface is illuminated one by one by photons of energy 2 eV and 4 eV respectively. The work function of the metal is 0.5 eV. What is the ratio of the maximum speeds of electrons emitted in two cases?

Solution:

In this problem we need to use the energy conservation. The work function of the metal can be considered as the potential energy of electron. Then the conservation law in the present problem takes the form: the energy of the photon is equal to the mechanical energy of electron:

The kinetic energy is

Then

and

Then the ratio of the speeds of the electrons in two cases is