Question

The wavelength of a spectral line emitted by hydrogen atom in the Lyman series is $\frac{16}{15R}cm$. 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,
$\frac{1}{\lambda }=R\left[\frac{1}{1^2}-\frac{1}{n_2^2}\right]$
$\frac{15R}{16}=R\left[\frac{1}{1^2}-\frac{1}{n_2^2}\right]$
$\frac{15R}{16R}=\left[\frac{n_2^2-1}{n_2^2}\right]$
$\frac{15}{16}=\frac{n_2^2-1}{n_2^2}$
$15n_2^2=16n_2^2-16$
$n_2^2=16$
$n_2=4$