Question

Read the passage given below and answer the question
The hydrogen-like species $L{i}^{2+}$ is in a spherically symmetric state $S_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state $S_2$. The state $S_2$ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.
The orbital angular momentum quantum number of the state $S_2$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (B)

The state $S_2$ has one radial node and its energy is equal to the ground state energy of the hydrogen atom. This is possible only for $3p$ orbital.
$3p$ orbital has one radial node,
$n=3$, $l=1\Rightarrow (n-l-1)=(3-1-1)=l$
$E=E_H\times \frac{Z^2}{n^2}$
$E_H\times \frac{3^2}{2^2}=E_H$
Azimuthal quantum number for the state $S_2$,$l=1$.