Question

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

Answer 1

Answer: 3

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 $\frac{hc}{\lambda .3}=\frac{hc}{{\lambda }_1}\left[\because E=\frac{hc}{\lambda }\right]$
or $\frac{1}{3\lambda }=\frac{1}{{\lambda }_1}$
or $\frac{{\lambda }_1}{\lambda }=3$
or ${\lambda }_1=3\lambda$