Question

For which of the following set of quantum numbers will an electron have the highest energy?

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

Answer 1

The correct option is C $n=4,l=1,m=-1,s=-\frac{1}{2}$

According to Aufbau principle, electrons are assigned to orbitals in order of increasing value of sum of $n+l$.
For two orbitals having same value of $n+l$, electrons will be assigned to the orbital having lowest value of $n$.
For option (a), $n+l$ = 4
For option (b), $n+l$ = 3
For option (c), $n+l$ = 5 and n = 4
For option (d), $n+l$ = 5 and n = 3
$\therefore$ For option (c) and option (d), $n+l$ value is same but value of n is more for option (c) hence it will have higher energy.