Question

Explain the meaning of work function of a photosensitive surface.

Hint:

It is the minimum energy to free an electron from the metal surface; \( W_0 = h\nu_0 \) with \( \nu_0 \) the threshold frequency.

Answer 1

Step 1 (Definition): The work function of a photosensitive (metal) surface is the minimum energy that must be supplied to a free electron so that it can just escape from the surface of the metal.

Step 2 (Why it is needed): Free electrons inside a metal are held back by the attractive forces of the positive ions. To pull an electron out of the surface, this binding must be overcome, and the least energy that does this is the work function, denoted \( W_0 \) (or \( \phi_0 \)).

Step 3 (Relation to threshold frequency): In the photoelectric effect it is related to the threshold frequency \( \nu_0 \) by
\[ W_0 = h \nu_0 \]
where \( h \) is Planck's constant. Light of frequency below \( \nu_0 \) cannot eject electrons. It is usually measured in electron-volt (eV).

\[\boxed{W_0 = h\nu_0 = \text{minimum energy to free an electron from the surface.}}\]