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}}$