Question

What is the degeneracy of the level of the hydrogen atom that has the energy $(-\frac{R_H}{9})$?

Answer 1

$E_n=-\frac{R_H}{n^2}=-\frac{R_H}{9}$
$\therefore$ $n=3$
Thus, $l=0$ and $m=0$ (one $3s$-orbital)
$l=1$ and $m=-1,0,+1$ (three $3p$-orbitals)
$l=2$ and $m=-2,-1,0,+1,+2$ (five $3d$-orbitals)
Thus, degeneracy is nine $(1+3+5=9states)$.