Question

The following diagram indicates the energy levels of a certain atom when the system moves from $4\, E$ level to $E$. A photon of wavelength $\lambda$, is emitted. The wavelength of photon produced during its transition from $\frac{7}{3} E$ level to 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} $

Answer 1

Answer: (B)

Transition from $4 E$ to $E$
$(4 E-E)=\frac{h c}{\lambda_{1}} $
$\Rightarrow \lambda_{1}=\frac{h c}{3 E} \ldots(i)$
Transition from $\frac{7}{3} E$ to $E$
$\left(\frac{7}{3} E-E\right)=\frac{h c}{\lambda_{2}} $
$\Rightarrow \lambda_{2}=\frac{3 h c}{4 E} \ldots(ii)$
From Eq. (i) and (ii)
$\frac{\lambda_{1}}{\lambda_{2}}=\frac{4}{9}$