Question

The given diagram indicates the energy level of a certain atom. When an electron moves from 2E level to E level, a photon of wavelength $\lambda$ is emitted. The wavelength of photon emitted during its transition from $\frac{4E}{3}$ level to E level is:
____ $2E$
____$\frac{4E}{3}$
____ $E$

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

Answer 1

The correct option is D $3\lambda$

When the electron jumps from $2E$ level to $E$ level, a photon of wavelength $\lambda$ is emitted. Thereby,
$hv=2E-E\frac{hc}{\lambda }=E\text{or}$
$\lambda =\frac{hc}{E}....\left(1\right)$
When the electron jumps from $\frac{4E}{3}$ level to E level, a photon of wavelength ${\lambda }_1$ is emitted. Thereby,
$hv=\frac{4E}{3}-E\frac{hc}{{\lambda }_1}=\frac{E}{3}\text{or}$
${\lambda }_1=\frac{3hc}{E}$
From equation 1,
${\lambda }_1=3\lambda$