Question

The energy of a $I,II$ and $III$ energy levels of a certain atom are $E,\frac{4E}{3}$ and $2E$ respectively. A photon of wavelength $\lambda$ is emitted during a transition from $III$ to $I$. What will be the wavelength of emission for transition $II$ to $I$?

• A. $\frac{\lambda }{2}$
• B. $\lambda$
• C. $2\lambda$
• D. $3\lambda$

Answer 1

The correct option is D $3\lambda$

For $II$ to $I$ transition,
$△E=\frac{4E}{3}-E\Rightarrow \frac{hc}{{\lambda }_{II\to I}};$

$\frac{E}{3}=\frac{hc}{{\lambda }_{II\to I}}$

For $III$ to $I$ transition,
$△E=2E-E=\frac{hc}{\lambda }$ or $E=\frac{hc}{\lambda }$
$\therefore \frac{hc}{3\times \lambda }=\frac{hc}{{\lambda }_{II\to I}}$

${\lambda }_{II\to I}=3\lambda$