Question

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

• A. $16$
• B. $9$
• C. $4$
• D. $1$

Answer 1

The correct option is B $9$

Energy of the electron in the $n$th orbit in terms of $R_H$ is:

$E_n=-\frac{R_H{Z}^2}{n^2}$

where, $Z=$ atomic number, $n^2=$ degeneracy

For $H$-atom,

$E_n=-\frac{R_H{\left(1\right)}^2}{n^2}$

$-\frac{R_H}{9}=-\frac{R_H}{n^2}$

$\therefore n^2=9$