Q. Which one of the following sets of quantum numbers represents the highest energy level in an atom?

A) $n = 4,\ l = 0,\ m = 0,\ s = + \frac{1}{2}$
B) $n = 3,l = 1,m = 1,s = + \frac{1}{2}$
C) $n = 3,\ l = 2,m = - 2,\ s = + \frac{1}{2}$
D) $n = 3,\ l = 0,\ m = 0,\ s = + \frac{1}{2}$
Explanation

(c)
$n = 4,\ l = 0,\ m = 0,s = + \frac{1}{2}$
$\rightarrow 4s$ energy level.
$n = 3,\ l = 1,\ m = - 1,\ s = + \frac{1}{2}$
$\rightarrow 3p$ energy level.
$n = 3,\ l = 2,\ m = - 2,\ s = + \frac{1}{2}$
$\rightarrow 3d$ energy level.
$n = 3,\ l = 0,\ m = 0,\ s = + \frac{1}{2}$
$\rightarrow 3s$ energy level.
According to aufbau principle, the energy of orbitals (other than H-atom) depend upon $n + 1$ value.
$n + l\ for\ 3d = 3 + 2 = 5$
So, it is highest energy level (in the given options).

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.