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

Answer: (A)

First time of paschen series $n_1=3,n_2=4$
$\frac{1}{{\lambda }_1}=R\left[\frac{1}{9}-\frac{1}{16}\right]$
$\frac{1}{{\lambda }_1}=\frac{7R}{144}$
${\lambda }_1=\frac{144}{7R}$
Second line of paschen series $n_1=3,n_2=5$
$\frac{1}{{\lambda }_2}=R\left[\frac{1}{9}-\frac{1}{25}\right]$
$\frac{1}{{\lambda }_2}=\frac{16R}{225}{\lambda }_2=\frac{225}{16R}$
$=\frac{{\lambda }_1}{{\lambda }_2}=\frac{144}{7R}\times \frac{16R}{225}$
$=\frac{2304}{1575}=\frac{256}{175}$