Question

Hydrogen atom from excited state comes to the ground by emitting a photon of wavelength $\lambda$. The value of principal quantum number 'n' of the excited state will be : (R : Rydberg constant)

• A. $\sqrt{\frac{\lambda R}{\lambda -1}}$
• B. $\sqrt{\frac{\lambda R}{\lambda R-1}}$
• C. $\sqrt{\frac{\lambda }{\lambda R-1}}$
• D. $\sqrt{\frac{\lambda R^2}{\lambda R-1}}$

Answer 1

Answer: (B)

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