17.1.4 Stopping Potential

If the collector is connected to the negative terminal of the variable power supply, it is said to be in negative bias. Electrically, the collector (being negatively charged) is now repulsive to the (negatively charged) photoelectrons. From the energy perspective, a negative bias establishes a potential energy barrier for the photoelelectrons.

Take for example a negative bias of 2.0 V, which establishes a potential energy barrier of 2.0 eV between the emitter and the collector[1]. This is because every photoelectron that travels from the emitter to the collector must gain 2.0 eV of EPE, which must come at the expense of losing 2.0 eV of KE. So 2.0 V negative bias will only allow photoelectron that are emitted with at least 2.0 eV of KE to be arrive at the collector. All the photoelectrons with 2.0 eV or lower KE do not have sufficient KE to overcome the energy barrier, and are returned to the emitter.

This explains why as we gradually increase the negative bias, the photoelectric current becomes smaller and smaller. The negative bias voltage at which the photoelectric current first drops to zero is called the stopping potential, Vs. From the fact that an energy barrier of eVs is insurmountable for all photoelectrons, we can deduce that the maximum KE of the photoelectrons is

$\displaystyle K{{E}_{{\max }}}=e{{V}_{s}}$

[1] The eV (electron-volt) is an energy unit. Just like $\displaystyle 1\text{ kWh}=(1000)(60\times 60)=3.6\text{ MJ}$, $\displaystyle 1\text{ eV}=(1)(1.60\times {{10}^{{-19}}})=1.60\times {{10}^{{-19}}}\text{ J}$.