Question

A spectral line in the Lyman series of hydrogen atom has a wave number of 82200 cm${}^{-1}$. Which of the following transition is responsible for the radiation?(R = 109600 cm${}^{-1}$)

• A. $n_1=1,n_2=2$
• B. $n_1=4,n_2=5$
• C. $n_1=4,n_2=6$
• D. $n_1=1,n_2=3$

Answer 1

The correct option is A $n_1=1,n_2=2$

$\nu =\frac{c}{\lambda }$
Thus, $\frac{1}{\lambda }=\frac{\nu }{c}=\frac{82200}{3\times {10}^{10}}=2.74\times {10}^{-6}$
But $\frac{1}{\lambda }=R[\frac{1}{n_1^2}-\frac{1}{n_2^2}$
For Lyman series, $n_1=1$
Substitute values in the above expression.
$2.74\times {10}^{-6}=109600\times [\frac{1}{1^2}-\frac{1}{n_2^2}$
Hence, $n_2=2$