Q. A hydrogen atom and a $Li^{+ +}$ion are both in second excited state. If $l_{H}\ and\ l_{Li}$ are their respective electronic angular momenta, and $E_{H}and\ E_{Li}$their respective energies, then
A) $l_{H} > l_{Li}and\ \left| E_{H} \right| > | > |E_{Li}\left. \ \ \right|$
B) $L_{H} = L_{i}and\ \left| E_{H} \right| < E_{Li}\left. \ \ \right|$
C) $l_{H} > l_{Li}and\ \left| E_{H} \right| > E_{Li}\left. \ \ \right|$
D) $l_{H} > l_{Li}and\ \left| E_{H} \right| < < E_{Li}\left. \ \ \right|$
Explanation
(b) In the second excited state, $n = 3$
$\therefore l_{H} = l_{Li} = 3\left( \frac{h}{2\pi} \right)$
As $E \propto Z^{2}$and $Z_{H} = 1,$ and $Z_{Li} = 3$
$\therefore\ \left| E_{Li} \right| = 9\left| E_{H} \right|\ \ or\ \ \left| E_{H} \right| < \left| E_{Li} \right|$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.