Question

An excited hydrogen atom emits a photon of wavelength $\lambda$ in returning to the ground state. If $R$ is the Rydberg constant, then the quantum number $n$ of the excited state will be:

• A. $\sqrt{\lambda R}$
• B. $\sqrt{\lambda R-1}$
• C. $\sqrt{\frac{\lambda R}{\lambda R-1}}$
• D. $\sqrt{\lambda R(\lambda R-1)}$

Answer 1

Answer: (C)

$\sqrt{\frac{\lambda R}{\lambda R-1}}$

As we know, $\frac{1}{\lambda }=R[\frac{1}{1^2}-\frac{1}{n^2}]$
$\frac{(n^2-1)}{n^2}=\frac{1}{\lambda R}$
$n=\sqrt{\frac{\lambda R}{\lambda R-1}}$

Hence, the correct option is $C$