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

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 $\lambda_{1} = 3\lambda$