Question

The wavelength (in cm) of second line in the Lyman series of hydrogen atomic spectrum is (Rydberg constant = R cm^-1)

• A. $\left(\frac{8R}{9}\right)$
• B. $\left(\frac{9}{8R}\right)$
• C. $\left(\frac{4}{3R}\right)$
• D. $\left(\frac{3R}{4}\right)$

Answer 1

Answer: (B)

$\vec{v}=\frac{1}{\lambda}=R\left[\frac{1}{n^{2}_{1}}-\frac{1}{n^{2}_{2}}\right]$
For second line in lyman series
n₂ = 3
$\therefore \frac{1}{\lambda}=R\left[\frac{1}{1^{2}}-\frac{1}{3^{2}}\right]=R\left[\frac{1}{1}-\frac{1}{9}\right]=\frac{8 R}{9}$
$\therefore \lambda=\frac{9}{8 R}$