Atomic Structure - Result Question 75

Passage Based Questions

The hydrogen-like species $\mathrm{Li}^{2+}$ 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.

51. The orbital angular momentum quantum number of the state $S _2$ is

(2010)

(a) $0$

(b) $1$

(c) $2$

(d) $3$

Show Answer

Answer:

Correct Answer: 51. (b)

Solution:

  1. In $S _2$ state, $E\left(Li^{2+}\right)=K$ (given)

$ K=\dfrac{q k}{n^{2}} $

$\Rightarrow \quad n =3$

Since, $S _2$ has one radial node.

$ \begin{aligned} 3-l-1 & =1 \\ l & =1 \end{aligned} $