Question

The wavelength of a spectral line emitted by hydrogen atom in the Lyman series is $\frac{16}{15 R} cm$. What is the value of $n_{2}$ ?
$(R=$ Rydberg constant $)$

• A. 2
• B. 3
• C. 4
• D. 1

Answer 1

Answer: (C)

For Lyman series,
$\frac{1}{\lambda }=R\left[ \frac{1}{{{1}^{2}}}-\frac{1}{n_{2}^{2}} \right]$
$\frac{15R}{16}=R\left[ \frac{1}{{{1}^{2}}}-\frac{1}{n_{2}^{2}} \right]$
$\frac{15R}{16R}=\left[ \frac{n_{2}^{2}-1}{n_{2}^{2}} \right]$
$\frac{15}{16}=\frac{n_{2}^{2}-1}{n_{2}^{2}} $
$15 n_{2}^{2}=16 n_{2}^{2}-16$
$n_{2}^{2}=16$
$n_{2}=4$