Question

For Balmer series, wavelength of first line is '${\lambda }_1$' and for Brackett series, wavelength of first line is '${\lambda }_2$' then $\frac{{\lambda }_1}{{\lambda }_2}$ is

• A. $0.081$
• B. $0.162$
• C. $0.198$
• D. $0.238$

Answer 1

The correct option is B $0.162$

First line of Balmer series is obtained when a transition takes place from $n_2=3$ to $n_1=2$.

$\therefore$ Wavelength of first line in Balmer series $\frac{1}{{\lambda }_1}=R[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$

$\therefore$ $\frac{1}{{\lambda }_1}=R[\frac{1}{2^2}-\frac{1}{3^2}]=\frac{5R}{36}$ ....(1)

First line of Brackett series is obtained when a transition takes place from $n_2=4$ to $n_1=5$.

$\therefore$ $\frac{1}{{\lambda }_2}=R[\frac{1}{4^2}-\frac{1}{5^2}]=\frac{9R}{400}$ ....(2)

Dividing equation (2) by (1), we get $\frac{{\lambda }_1}{{\lambda }_2}=\frac{9R/400}{5R/36}=0.162$