Question
Which of the following sets of quantum numbers represents the highest energy of an atom?
A.
$${\text{n = 3, 1 = 0, m = 0, s = + }}\frac{1}{2}$$
B.
$${\text{n = 3, 1 = 1, m = 1, s = + }}\frac{1}{2}$$
C.
$${\text{n = 3, 1 = 2, m = 1, s = + }}\frac{1}{2}$$
D.
$${\text{n = 4, 1 = 0, m = 0, s = + }}\frac{1}{2}$$
Answer :
$${\text{n = 3, 1 = 2, m = 1, s = + }}\frac{1}{2}$$
Solution :
$$\eqalign{
& n{\text{ = 3,}}\,l = 0\,{\text{means 3s - orbital and}}\,n + 1 = 3 \cr
& n{\text{ = 3,}}\,l = 1\,{\text{means 3p - orbital }}n + 1 = 4 \cr
& n{\text{ = 3,}}\,l = 2\,{\text{means 3d - orbital }}n + 1 = 5 \cr
& n{\text{ = 4,}}\,l = 0\,{\text{means 4s - orbital }}n + 1 = 4 \cr} $$
Increasing order of energy among these orbitals is
$$3s< 3p< 4s< 3d$$
∴ $$3d$$ has highest energy.