Question

A hydrogen atom and $L{i}^{++}$ ion are both in the second excited state. If $l_H$ and $l_{Li}$ are their respective electronic moments, and $E_H$ and $E_{Li}$ their respective energies, then

• A. $l_H>l_{Li}and\Vert E_H\Vert >\Vert E_{Li}\Vert$
• B. $l_H=l_{Li}and\Vert E_H\Vert <\Vert E_{Li}\Vert$
• C. $l_H=l_{Li}and\Vert E_H\Vert >\Vert E_{Li}\Vert$
• D. $l_H<l_{Li}and\Vert E_H\Vert <\Vert E_{Li}\Vert$

Answer 1

Answer: (B)

According to Bohr, the angular momentum of an electron of hydrogen atom and hydrogen like atom Li${}^{++},$ $l=n\frac{h}{2\pi }$.
For both, $n$ = 2 $\therefore$ $l_H=l_{Li}=2\times \frac{h}{2\pi }=\frac{h}{\pi }$
Energy of electron in nth orbit of hydrogen atom, $E_H=-\frac{13.6}{n^2}$ eV
For $n$ = 2, we get $E_H=-\frac{13.6}{4}$ - 3.4 eV
Energy of electron in nth orbit of hydrogen like atom (say Li${}^{++}$ ion), $E_{Li}=\frac{Z^2\times 13.6}{n^2}$ eV
Here $n$ = 2 and for Li, Z = 3 $\therefore$ $E_{Li}=\frac{9\times 13.6}{4}$ = - 30.6 eV
$i.e.$ $|E_H|<|E_{Li}|$