# GRE GR 1777, Problem 010 Solution

Physics GRE GR 1777

10. Quantum Mechanics (Photoelectric effect)

Solution)

The maximum kinetic energy of the emitted electrons is

$E_{max} = h\nu -w$,
where $E_{max}$ is the maximum kinetic energy of the emitted electrons from the metal surface, $\nu$ is the frequency of light, and $w$ is the work function of the metal.

Also, if we want to stop the emitted electrons, we should put some potential difference onto them. Thus, the previous equation becomes

$E_{max} = h\nu -w = qV$,
where $q$ is the electric charge, in this problem, should be $e$. In this equation, we can prove that the potential difference is a linear function of the frequency.