Question

An excited hydrogen atom emits a photon of wavelength $\lambda$ in returning to the ground state. The shell $n$ of the excited state is given by: $(R=Rydbergconstant)$.

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

Answer 1

The correct option is B $\sqrt{\frac{\lambda R}{(\lambda R-1)}}$

We know that, $\frac{1}{\lambda }=R[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$

$n_1$=lowest orbit

$n_2$=highest orbit

Here, $n_1$=ground state=1

$n_2$=we have to find

$\frac{1}{\lambda R}=[\frac{1}{1}-\frac{1}{n_2^2}]⟹\frac{1}{n_2^2}=1-\frac{1}{\lambda R}\therefore n_2=\sqrt{\frac{\lambda R}{\lambda R-1}}$