Question

The $\lambda$ of $H_{\alpha}$ line of the Balmer series is $6500\, \mathring{A}$. What is the $\lambda$ of $H_{\beta}$ line of the Balmer series?

Answer 1

For $H_{\alpha}$ line of the Balmer series, $n_{1} =2, n_{2} =3$.
For $H_{\beta}$ line of the Balmer series, $_{1} =2, n_{2} =4$.
$\therefore \frac{1}{\lambda_{H_{\alpha}}} = R_{H}\left[\frac{1}{2^{2}} -\frac{1}{3^{2}}\right] .....\left(i\right)$
and $\frac{1}{\lambda_{H\beta}} = R_{H} \left[\frac{1}{2^{2}} -\frac{1}{4^{2}}\right] ...\left(ii\right)$
By equations (i) and (ii), we get
$\therefore \frac{\lambda_{\beta}}{\lambda_{\alpha}} = \frac{\frac{1}{4} -\frac{1}{9}}{\frac{1}{4} -\frac{1}{16}}$
$\therefore \lambda_{\beta} = \lambda_{\alpha}\times\left[\frac{80}{108}\right] $
$=6500\times\frac{80}{108} = 4814.8\, \mathring{A}$