Question

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

(a) n = 3, l = 1, m = 1, s = +1/2

(b) n = 3, l = 2, m = 1, s = +1/2

(c) n = 4, l = 0, m = 0, s = +1/2

(d) n = 3, l = 0, m = 0, s = +1/2

Answer 1

Correct option is (b) n = 3, l = 2, m = 1, s = +1/2

According to (n + l) rule, the energy of an orbital depends upon the sum of the values of the principal quantum number (n) and the azimuthal quantum number (l). Lower the value of (n + l), lower is the energy. If two different orbitals have the same value of (n + l), the orbital with lower value of n has lower energy.

In option (a), (n + l) = 3 + 1 = 4

In option (b), (n + l) = 3 + 2 = 5

In option (c), (n + l) = 4 + 0 = 4

In option (d), (n + l) = 3 + 0 = 3

Thus highest energy level is depicted in option (b).