Question

A hydrogen atom and a $L{i}^{++}$ 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

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

Answer 1

Answer: (B)

$l_H=l_{Li}$ and $E_H<|E_{Li}|$

Given $Z_H=1,Z_{Li}=3$ and $n_H=n_{Li}=3$
1. Angular momentum is independent of Z, therefore $l_H=l_{Li}$
2. Energy is directly proportional to square of atomic number, hence $E_H<E_{Li}$