Question

Calculate ionization potential and first excitation potential of the hydrogen

atom taking ℎ = 6.62 x 10−34𝐽𝑠, 𝑒 = 1.6 x 10−19

, 𝑚 = 9.1 x 10−31𝑘𝑔.

Answer 1

The ionization potential of the hydrogen atom is the energy required to remove one electron at the ground state from the atom. We can use Rydberg equation:

$$\frac1\lambda=R\bigg(\frac{1}{n_1^2}-\frac{1}{n_\infty^2}\bigg)=\frac{R}{n_1^2},\\\space\\ E_0=h\nu=h\frac c\lambda=hRc=2.18\cdot10^{-18}\text{ J, or 13.6 eV.}$$

The first excitation potential of the hydrogen atom is

$$V=\frac{3}{4}E_0=\frac34\cdot13.6=10.2\text{ eV}.$$