Question

The wavelength of a spectral line emitted by hydrogen atom in the Balmer series is $\frac{16}{3 R}$ ( $R$ is Rydberg constant). What is the value of the principal quantum number of the state from which the transition takes place?

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (C)

In spectral line series, wavelength is given by
$\frac{1}{\lambda}=R\left(\frac{1}{n_{f}^{2}}-\frac{1}{n_{i}^{2}}\right)$
For Balmer transitions,

$\Rightarrow \frac{1}{\lambda}=R\left(\frac{1}{4}-\frac{1}{n^{2}}\right)$
Given, $\lambda=\frac{16}{3 R}$
$\Rightarrow \frac{3 R}{16}=R\left(\frac{1}{4}-\frac{1}{n^{2}}\right) $
$\Rightarrow \frac{3}{16}=\frac{1}{4}-\frac{1}{n^{2}}$
$\Rightarrow \frac{1}{n^{2}}=\frac{1}{4}-\frac{3}{16}=\frac{1}{16}$
$ \Rightarrow n=4$