Thermionic emission

When a material such as a metal is heated, some of its electrons can gain enough energy to escape from its surface. This release of electrons is called thermionic emission.

Electrons in the material are held there by attractive forces. To leave the surface, an electron must have enough energy to overcome that attraction. The minimum energy needed for an electron to escape is called the material’s work function.

Heating supplies energy to the electrons, but they do not all have the same energy. Only those with enough energy to overcome the work function can escape. Increasing the temperature increases the number of electrons with sufficient energy, so more electrons are emitted.

Electron acceleration through a potential difference

An electric field exerts a force on an electron. If the electron moves in the direction of that force, the field does work on it and the electron gains kinetic energy.

For an electron accelerated through a potential difference $$V$$, the work done by the electric field is:

Here, $$e$$ is the magnitude of the electron’s charge, so it is positive even though the electron’s charge is negative. The accelerating potential difference $$V$$ is also taken as a positive value. If all the work done becomes kinetic energy, the electron gains energy $$eV$$.

Electron speed from rest

If the electron starts from rest, its initial kinetic energy is zero. Its final kinetic energy is therefore equal to the work done by the field:

Here, $$m$$ is the electron’s mass and $$v$$ is its final speed. This kinetic-energy expression applies when the speed is well below the speed of light.

A larger accelerating potential difference means more work is done on the electron. It therefore gains more kinetic energy and, starting from rest, reaches a greater speed.