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 =R h c\left(1-\frac{1}{n^{2}}\right) $
or $ \frac{h c}{\lambda} =R h c\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)}$