Question

How do you calculate ionization energy using Rydberg constant?

Answer 1

The Rydberg equation for absorption is

$\frac{1}{\lambda }=R(\frac{1}{n_i^2}-\frac{1}{n_f^2})$

Where $v$ is the wavelength of the absorbed photon, $R$ is the Rydberg constant, $n_i$ denotes the energy level the electron started in, and $n_f$ the energy level it ends up in.

We are calculating ionization energy so the electron goes to infinity with respect to the atom, ie it leaves the atom. Hence we set $n_f=\infty$

Assuming we ionize from the ground state, we set $n_i=1$

$\frac{1}{\lambda }=R$

$E=\frac{hc}{\lambda }\Rightarrow E=hcR$

$E=6.626\times {10}^{-34}\times 3\times {10}^8\times 1.097\times {10}^7=2.182\times {10}^{-18}J$

$1eV=1.6\times {10}^{-19}J$ so to convert to $eV$ we divide by $1.6\times {10}^{-19}$

$\frac{2.182\times {10}^{-18}}{1.6\times {10}^{-19}}=13.6eV$