Q. Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelengths $\lambda_{1}:\lambda_{2}$ emitted in the two cases is
A) $7/5$
B) $27/20$
C) $27/5$
D) $20/7$
Explanation
(d) [image:13_image28.emf]
$E_{1} = \frac{hc}{\lambda_{1}} = 13.6\left\lbrack \frac{1}{(3)^{2}} - \frac{1}{(4)^{2}} \right\rbrack$ …(i)
$E_{2} = \frac{hc}{\lambda_{2}} = 13.6\left\lbrack \frac{1}{(2)^{2}} - \frac{1}{(3)^{2}} \right\rbrack$ …(ii)
Dividing eq. (ii) by eq. (i)
$\frac{\lambda_{1}}{\lambda_{2}} = \frac{\frac{1}{4} - \frac{1}{9}}{\frac{1}{9} - \frac{1}{16}} = \frac{20}{7}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.