Question

What will be the ratio of the wavelength of the first line to that of the second line of Paschen Series of $H$ atom ?

• A. $256:175$
• B. $175:256$
• C. $15:16$
• D. $24:27$

Answer 1

The correct option is A $256:175$

First line of Paschen Series,
$n_1=3,n_2=4$
$\frac{1}{{\lambda }_1}=R[\frac{1}{9}-\frac{1}{16}]$
$\Rightarrow {\lambda }_1=\frac{9\times 16}{7R}$
Second line of Paschen Series,
$n_1=3,n_2=5$
$\frac{1}{{\lambda }_2}=R[\frac{1}{9}-\frac{1}{25}]$
${\lambda }_2=\frac{9\times 25}{16R}$
$\therefore \frac{{\lambda }_1}{{\lambda }_2}=\frac{256}{175}$