Question

The energy levels of a certain atom for 1st, 2nd and 3rd levels are E, $\frac{4E}{3}$ and 2E respectively. A photon of wavelength $\lambda$ is emitted for a transition $3\to 1$. What will be the wavelength of emissions for transition $2\to 1$

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

Answer 1

The correct option is D $3\lambda$

For transition $3\to 1$ $\Delta E=2E-E=\frac{hc}{\lambda }\Rightarrow E=\frac{hc}{\lambda }$ ....... (i)
For transition $2\to 1$ $\frac{4E}{3}-E=\frac{hc}{{\lambda }^{{}^{\prime }}}\Rightarrow E=\frac{3hc}{{\lambda }^{{}^{\prime }}}$ ....... (ii)
From equation (i) and (ii) ${\lambda }^{{}^{\prime }}=3\lambda$