Question

A hydrogen atom is in an excited state of principle quantum number $n$. It emits a photon of wavelength ${}^{\prime }\lambda {}^{\prime }$ when it returns to the ground state. The value of ${}^{\prime }n{}^{\prime }$ is

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

Answer 1

The correct option is C $\sqrt{\frac{\lambda R}{\lambda R-1}}$

$\frac{1}{\lambda }=R(1-\frac{1}{n^2})$
$n^2=\frac{\lambda R}{\lambda R-1}$
$n=\sqrt{\frac{\lambda R}{\lambda R-1}}$