Question

The ratio of the wavelengths of last lines of Balmer and Lyman series is:

• A. $4:1$
• B. $27:5$
• C. $3:1$
• D. $9:4$

Answer 1

The correct option is A $4:1$

The wave length of a spectral line may be given by the following expression
$\frac{1}{\lambda }=R(\frac{1}{n_1^2}-\frac{1}{n_2^2})$
For Lyman series, $n_1=1$, For Balmer series, $n_1=2$
For the last line in both the series $n_2=\infty$
For Lyman series.
$\frac{1}{{\lambda }_L}=R(1-\frac{1}{\infty })=R(1-0)=R$
${\lambda }_L=\frac{1}{R}$
For Balmer series,
$\frac{1}{{\lambda }_B}=R(\frac{1}{4}-\frac{1}{\infty })=\frac{R}{4}{\lambda }_B=\frac{4}{R}$
$\frac{{\lambda }_B}{{\lambda }_L}=\frac{4}{R}\times \frac{R}{1}=\frac{4}{1}$