Question

An excited hydrogen atom returns to the ground state. the wavelength photon is $\gamma$. The principal quantum number of the excited will be:

• A. ${\left[\frac{\gamma R}{\gamma R-1}\right]}^{1/2}$
• B. ${\left[\frac{\gamma R+1}{\gamma R}\right]}^{1/2}$
• C. ${\left[\gamma R\right(\gamma R+1\left)\right]}^{1/2}$
• D. ${\left[\frac{1}{\gamma R(\gamma R+1)}\right]}^{1/2}$

Answer 1

Answer: (A)

${\left[\frac{\gamma R}{\gamma R-1}\right]}^{1/2}$

The correct answer is $\left(A\right)=\sqrt{\frac{\gamma R}{\gamma R-1}}$

AS

$\frac{1}{\gamma }=R\left(\frac{1}{1^2}-\frac{1}{n^2}\right)$

$\frac{1}{\gamma R}=1-\frac{1}{n^2}or\frac{1}{n^2}=1-\frac{1}{\gamma R}=\frac{\gamma R-1}{\gamma R}$

$n=\sqrt{\frac{\gamma R}{\gamma R-1}}$

$={\left(\frac{\gamma R}{\gamma R-1}\right)}^{\frac{1}{2}}$

Hence, the given answer $\left(A\right)$ is correct