Question

If ${\lambda }_1$ and ${\lambda }_2$ are the wavelengths of the first members of the Lyman and Paschen series respectively, then ${\lambda }_1:{\lambda }_2$ is

• A. 1 : 3
• B. 1 : 30
• C. 7 : 50
• D. 7 : 108

Answer 1

Answer: (D)

For first line of Lyman series,
$n_1=1$ and $n_2=2$
$\therefore \frac{1}{{\lambda }_1}=R\left(\frac{1}{1^2}-\frac{1}{2^2}\right)$
$=R\left(1-\frac{1}{4}\right)=\frac{3R}{4}$
For first line of Paschen series $n_1=3$ and $n_2=4$
$\therefore \frac{1}{{\lambda }_2}=R\left(\frac{1}{3^2}-\frac{1}{4^2}\right)$
$=R\left(\frac{1}{9}-\frac{1}{16}\right)=\frac{7R}{144}$
$\frac{{\lambda }_1}{{\lambda }_2}=\frac{7R}{144}\times \frac{4}{3R}$
$=\frac{7}{108}$