Physics - Modern Physics Question with Solution | TestHub

According to Rydberg formula

$\frac{1}{\lambda }=R\left[\frac{1}{n_f^2}-\frac{1}{n_i^2}\right]$

In first case, n_f= 3, n_i= 4

$\therefore \frac{1}{{\lambda }_1}=R\left[\frac{1}{3^2}-\frac{1}{4^2}\right]=R\left[\frac{1}{9}-\frac{1}{16}\right]=\frac{7}{144}R\dots \left(\text{i}\right)$

In second case, n_f= 2, n_i= 3

$\therefore \frac{1}{{\lambda }_2}=R\left[\frac{1}{2^2}-\frac{1}{3^2}\right]=R\left[\frac{1}{4}-\frac{1}{9}\right]=\frac{5}{36}R\dots \left(\text{i}\text{i}\right)$

Divide (ii) by (i) we get

$\frac{{\lambda }_1}{{\lambda }_2}=\frac{5}{36}\times \frac{144}{7}=\frac{20}{7}$