Physics - Modern Physics Question with Solution | TestHub

The wavelength of a line in Balmer series is given by
$\frac{1}{\lambda }=R\left(\frac{1}{2^2}-\frac{1}{n^2}\right)$[for n = 3, 4, 5,….]
Where, R= Rydberg constant.
For first line, n = 3
$\Rightarrow \frac{1}{{\lambda }_1}=R\left(\frac{1}{4}-\frac{1}{9}\right)\Rightarrow {\lambda }_1=\frac{35}{5R}$….(i)
The wavelength of a line in Brackett series is given by
$\frac{1}{\lambda }=R\left(\frac{1}{4^2}-\frac{1}{n^2}\right)$[for n = 5, 6, 7]
For first line, n = 5
$\Rightarrow \frac{1}{{\lambda }_2}=R\left(\frac{1}{16}-\frac{1}{25}\right)\Rightarrow {\lambda }_2=\frac{400}{9R}$……(ii)
Dividing Eq. (i) by Eq. (ii), we get
$\frac{{\lambda }_1}{{\lambda }_2}=\frac{36}{5R}\times \frac{9R}{400}=\frac{81}{500}=0.162$