Q. The following diagram indicates the energy levels of a certain atom when the system moves from $4E$ level to $E$. A photon of wavelength $\lambda_{1}$ is emitted. The wavelength of photon produced during it’s transition from $\frac{7}{3}E$ level to $E$ is $\lambda_{2}$. The ratio $\frac{\lambda_{1}}{\lambda_{2}}$ will be
A) $\frac{9}{4}$
B) $\frac{4}{9}$
C) $\frac{3}{2}$
D) $\frac{7}{3}$
Explanation
(b) Transition from $4E$ to $E$
$(4E - E) = \frac{hc}{\lambda_{1}} \Rightarrow \lambda_{1} = \frac{hc}{3E}$ …(i)
Transition from $\frac{7}{3}E$ to $E$
$\left( \frac{7}{3}E - E \right) = \frac{hc}{\lambda_{2}} \Rightarrow \lambda_{2} = \frac{3hc}{4E}$ …(ii)
From equation (i) and (ii), $\frac{\lambda_{1}}{\lambda_{2}} = \frac{4}{9}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.