Question

The energy levels of a certain atom for first, second and third levels are $E, 4 \frac{E}{3}$ and $2 E$ respectively. A photon of wavelength $\lambda$ is emitted for a transition $3 \rightarrow 1$. What will be the wavelength of emission for transition $2 \rightarrow 1 ?$

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

Answer 1

Answer: (B)

$\Delta E=2 E-E=\frac{h c}{\lambda_{1}}$
$\therefore E=\frac{h c}{\lambda_{1}}$
Similarly $\frac{4 E}{3}-E=\frac{h c}{\lambda_{2}}$
$\therefore \frac{E}{3}=\frac{h c}{\lambda_{2}} $
$\therefore \lambda_{2}=3 \lambda_{1}$