Question

The given diagram indicates the energy levels of certain atoms. When the system moves from the 2E level to E a photon of wavelength $\lambda$ is emitted. The wavelength 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

Answer: (D)

The explanation for the correct option

Option 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​ $[{\lambda }_1$ is the wave length of photon emitted]

or $\frac{4}{3}E-E=\frac{hc}{\lambda }$

$\frac{1}{3}E=\frac{hc}{{\lambda }_1}⟹\left(1\right)\because E=\frac{hc}{\lambda }putitinthisequation\left(1\right)$

$\frac{1}{3}\frac{hc}{\lambda }=\frac{hc}{{\lambda }_1}$

$\frac{1}{3\lambda }=\frac{1}{\lambda }$

$\therefore {\lambda }_1=3\lambda$

Hence, Option(D) $3\lambda$ The wavelength of photon produced during its transition from $\frac{4}{3}E$ level to $E$ level.