Question

In terms of Rydberg's constant $R$, the wavenumber of first line of Balmer series is,

• A. $R$
• B. $3R$
• C. $\frac{5R}{36}$
• D. $\frac{8R}{9}$

Answer 1

The correct option is C $\frac{5R}{36}$

Wave number, $\frac{1}{\lambda }=R[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$
For first line of Balmer series,
$n_1=2,n_2=3$

$\therefore \text{Wave number}=\frac{1}{\lambda }=R[\frac{1}{2^2}-\frac{1}{3^2}]$
$=\left(\frac{9-4}{9\times 4}\right)=\frac{5R}{36}$

Hence, $\left(C\right)$ is the correct answer.

Why this Question? This question is based on wavelength and wave number of emitted radiation.