and confirmed the wave-nature of electrons. The de Broglie hypothesis of matter waves supports the Bohr’s concept of stationary orbits. Physical Symbol Dimensions Unit Remarks Quantity Planck’s h [ML T – ] J s E = h + constant Stopping V [ML T – A – ] V e V = K max potential Work - [ML T – ] J; eV K max = E – - function Threshold + [T – ] Hz + = - / h frequency de Broglie # [L] = h/p wavelength POINTS TO PONDER . Free electrons in a metal are free in the sense that they move inside the metal in a constant potential (This is only an approximation).
They are not free to move out of the metal. They need additional energy to get out of the metal. . Free electrons in a metal do not all have the same energy.
Like molecules in a gas jar, the electrons have a certain energy distribution at a given temperature. This distribution is different from the usual Maxwell’s distribution that you have learnt in the study of kinetic theory of gases. You will learn about it in later courses, but the difference has to do with the fact that electrons obey Pauli’s exclusion principle. .
Because of the energy distribution of free electrons in a metal, the energy required by an electron to come out of the metal is different for different electrons. Electrons with higher energy require less additional energy to come out of the metal than those with lower energies. Work function is the least energy required by an electron to come out of the metal.