Question

The given diagram indicates the energy levels of certain atoms. When the systemmoves from 2E level to E a photon of wave length $\lambda$ is emitted. The wave - length of photon produced during its transition from $\frac{4E}{3}$ level to E is

• A. $\frac{\lambda }{3}$
• B. $\frac{3\lambda }{3}$
• C. $\frac{4}{3}\lambda$
• D. $3\lambda$

Answer 1

The correct option is D

$3\lambda$

From the given data, when the system moves from 2E level to E level, we have
$2E-E=\frac{hc}{\lambda }$
or $E=\frac{hc}{\lambda }$
When the system moves from $\frac{4E}{3}$ level to E level, we have
$\frac{4}{3}E-E=\frac{hc}{{\lambda }_1}$ $[{\lambda }_1$ is the wave length of photon emitted]
or $\frac{E}{3}=\frac{hc}{{\lambda }_1}$
or $\frac{hc}{\lambda .3}=\frac{hc}{{\lambda }_1}$ $[\because E=\frac{hc}{\lambda }]$
or $\frac{1}{3\lambda }=\frac{1}{{\lambda }_1}$
or ${\lambda }_1=3\lambda$