Question

The following diagram indicates the energy levels of a certain atom when the system moves from $4E$ level to $E$. A photon of wavelength $\lambda$, 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 $4E$ to $E$
$(4E-E)=\frac{hc}{{\lambda }_1}$
$\Rightarrow {\lambda }_1=\frac{hc}{3E}\dots (i)$
Transition from $\frac{7}{3}E$ to $E$
$\left(\frac{7}{3}E-E\right)=\frac{hc}{{\lambda }_2}$
$\Rightarrow {\lambda }_2=\frac{3hc}{4E}\dots (ii)$
From Eq. (i) and (ii)
$\frac{{\lambda }_1}{{\lambda }_2}=\frac{4}{9}$