Question

The following diagram indicated 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 emitted during its 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. $\frac{7}{3}$
• C. $\frac{4}{9}$
• D. $\frac{3}{2}$

Answer 1

The correct option is C $\frac{4}{9}$


Transition from $4E$ level to $E$ -

$4E-E=\frac{hc}{{\lambda }_1}$

$\Rightarrow {\lambda }_1=\frac{hc}{3E}...\left(i\right)$

Transition from $\frac{7}{3}E$ level to $E$ -

$\frac{7}{3}E-E=\frac{hc}{{\lambda }_2}$

$\Rightarrow {\lambda }_2=\frac{3hc}{4E}...\left(ii\right)$

From equations $\left(i\right)$ and $\left(ii\right)$,

$\frac{{\lambda }_1}{{\lambda }_2}=\frac{4}{9}$

Hence, option $\left(B\right)$ is the correct answer.