Question

What is the colour corresponding to the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from n=$4$ to n =$2$ ?

Answer 1

Wavelength $=?$

$\frac{1}{\lambda }=R_H(\frac{1}{n_1^2}-\frac{1}{n_2^2})$

$\frac{1}{\lambda }=R_H(\frac{1}{2^2}-\frac{1}{4^2})$

$=R_H(\frac{1}{4}-\frac{1}{16})$

$\frac{1}{\lambda }=R_H\times \frac{12}{16}$

$\frac{1}{\lambda }=\frac{3R_H}{4}$

$\lambda =\frac{4}{3R_H}=\frac{4}{3\times 109677}$cm $=1.212\times {10}^{-5}$

$=121.2$nm.