Question

The degeneracy of hydrogen atom that has energy equal to $\frac{-R_H}{9}$ is:
[where $R_H=$ Rydberg constant]

• A. $6$
• B. $8$
• C. $5$
• D. $9$

Answer 1

The correct option is D $9$

Energy in H-atom
$E=\frac{R_H}{n^2}$

But, given that $E=\frac{R_H}{9}$

⇒$n^2=9$

$n=3$

As here $n=3$ thus there are 3 orbits.

In general, for any energy level n, the degeneracy is given by n2

So when n= 3, the degeneracy is 9.

When n=3, the possible combinations of (n,l.m) are (3, 2, -2), (3,2, -1), (3, 2, 0), (3, 2, 1), (3, 2, 2), (3, 1, -1), (3, 1, 0), (3, 1, 1), and (3, 0, 0)

Hence D is the correct answer.