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

The correct option is D 7 : 108

Rydberg formula: $\frac{1}{\lambda }=R(\frac{1}{{n_1}^2}-\frac{1}{{n_2}^2})$

$n_1=$ 1 for lyman series

$n_1=$ 3 for Paschen series

$n_2=$ 2 for first member of lyman series

$n_2=$ 4 for first member of paschen series

$\Rightarrow \frac{\frac{1}{{\lambda }_1}}{\frac{1}{{\lambda }_2}}=\frac{R(\frac{1}{{n_1}^2}-\frac{1}{{n_2}^2})}{R(\frac{1}{{n_2}^2}-\frac{1}{{n_1}^2})}=\frac{(\frac{1}{1^2}-\frac{1}{2^2})}{(\frac{1}{3^2}-\frac{1}{4^2})}=\frac{108}{7}$

$\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\frac{7}{108}$