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

Answer: 4814.8

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
$\therefore \frac{{\lambda }_{\beta }}{{\lambda }_{\alpha }}=\frac{\frac{1}{4}-\frac{1}{9}}{\frac{1}{4}-\frac{1}{16}}$
$\therefore {\lambda }_{\beta }={\lambda }_{\alpha }\times \left[\frac{80}{108}\right]$
$=6500\times \frac{80}{108}=4814.8\mathring{A}$