Q. If $\lambda$ is the wavelength of hydrogen atom from the transition $n$ =3 to $n$=1, then what is the wavelength for doubly ionised lithium ion for same transition?
A) $\frac{\lambda}{3}$
B) 3$\lambda$
C) $\frac{\lambda}{9}$
D) 9 $\lambda$
Explanation
(c) For wavelength
$\ \ \ \ \ \ \ \ \ \ \ \ \frac{1}{\lambda} = {RZ}^{2}\left( \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right)$
Here, transition is same
So, $\ \ \ \ \ \lambda \propto \frac{1}{Z^{2}}$
$\ \ \ \ \ \ \ \ \ \frac{\lambda_{H}}{\lambda_{Li}} = \frac{\left( Z_{Li} \right)^{2}}{\left( Z_{H} \right)^{2}} = \frac{(3)^{1}}{(\ 1)^{2}} = 9$
$\ \ \ \ \ \ \ \ \ \lambda_{Li} = \frac{\lambda_{H}}{\ 9} = \frac{\lambda}{9}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.