Q.Explain thermionic (thermal) emission of electrons from a hot metal surface and state the factors on which the rate of emission depends.

Every free electron in a metal is held in by an energy barrier at the surface, the work function $\phi$. At ordinary temperature almost no electron has enough energy to cross it. Heating the metal (typically $1000$-$2500\ \text{K}$) gives a much larger fraction of electrons enough thermal energy to escape into the surrounding vacuum -- thermionic emission. The rate depends chiefly on temperature (rising very steeply with it) and on the work function (a lower $\phi$ gives more emission at the same temperature), which is why real cathodes use a low-work-function coating rather than plain tungsten.

State the work-function barrier idea, then name the two governing factors: temperature and work function.

• Saying electrons are 'pulled out' by a field -- thermionic emission needs no external field at all, only heat.
• Forgetting the emission rate is not linear in temperature -- it rises very steeply (almost exponentially).