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
(a) `l_H gt l_(Li) and |E_H| gt |E_(Li)|`
(b) `l_H = l_(Li) and |E_H| lt |E_(Li)|`
(C ) `l_H = l_(Li) and |E_H| gt |E_(Li)|`
(d) `l_H lt l_(Li) and |E_H| lt|E_(Li)|`

Options

A. `l_(H) gt l_(Li)` and `|E_(H)|gt|E_(Li)|`
B. `l_(H) = l_(Li)` and `|E_(H)|lt|E_(Li)|`
C. `l_(H) = l_(Li)` and `|E_(H)|gt|E_(Li)|`
D. `l_(H) lt l_(Li)` and `|E_(H)|lt|E_(Li)|`

Answer

B

Explanation

In second excited state `n = 3`
So `l_(H) = l_(Li) = 3((h)/(2pi))`
While `E prop Z^(2)` and `Z_(H) = 1, Z_(Li) = 3`
So `|E_(Li)| = 9|E_(H)|`or `|E_(H)|lt|E_(Li)|`