Potassium , like sodium , is an alkali metal, its single valence electron moving around a filled 18-electron argon-like core. As in sodium, there is a potassium doublet, its wavelengths being 764.5 nm and 769.9 nm. We have to calculate (a) the energy splitting between the upper two states and (b) the energy difference between the uppermost state and the ground state.

The wavelengths of the potassium doublets are

(a)

As the doublets arise because of transitions from the upper two states to the ground state, the energy splitting of the upper two states will therefore be

(b)

The energy difference between the uppermost state and the ground state will be equal to the energy of the photon of wavelength 764.5 nm. It is