Question

A hydrogen atom is in excited state of principal quantum number $n$. It emits a photon of wavelenth $\lambda$ when returns to ground state. The value of $n$ 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

Answer: (C)

Energy of photon
$E=Rhc\left(1-\frac{1}{n^2}\right)$
or $\frac{hc}{\lambda }=Rhc\left(1-\frac{1}{n^2}\right)$
or $\frac{1}{\lambda }=R\left(1-\frac{1}{n^2}\right)$
or $\frac{1}{\lambda R}=1-\frac{1}{n^2}$
or $\frac{1}{n^2}=1-\frac{1}{\lambda R}$
or $=\frac{(\lambda R-1)}{\lambda R}$
or $n=\sqrt{\lambda R/(\lambda R-1)}$