Modern Physics 1 Question 22
19. A hydrogen atom and a $Li^{2+}$ ion are both in the 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
(2002, 2M)
(a) $l _H>l _{Li}$ and $\left|E _H\right|>\left|E _{Li}\right|$
(b) $l _H=l _{Li}$ and $\left|E _H\right|<\left|E _{Li}\right|$
(c) $l _H=l _{Li}$ and $\left|E _H\right|>\left|E _{Li}\right|$
(d) $l _H<l _{Li}$ and $\left|E _H\right|<\left|E _{Li}\right|$
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Solution:
- In second excited state $n=3$,
$$ \begin{array}{ll} \text { So, } & l _H=l _{Li}=3 \frac{h}{2 \pi} \\ \text { while } & E \propto Z^{2} \\ \text { and } & Z _H=1, Z _{Li}=3 \end{array} $$
$$ \begin{array}{ll} \text { So, } & \left|E _{Li}\right|=9\left|E _H\right| \\ \text { or } & \left|E _H\right|<\left|E _{Li}\right| \end{array} $$
