Which of the following electronic configuration would be associated with the highest magnetic moment?

Solution

Chemistry ma’am · 3 steps

Magnetic moment comes from unpaired electrons, so fill the five d orbitals and count the singles.

1. What decides it. The spin-only magnetic moment depends only on n, the number of unpaired electrons. More unpaired electrons give a larger moment.

   μ = √n(n+2) BM

2. Fill by Hund's rule. Put one electron in each of the five d orbitals first. Pairing starts only from the sixth electron, so unpaired electrons peak at d⁵ and fall after that.

   Configuration	Unpaired electrons n	μ (BM)
   3d⁷	5 singles, 2 paired: n = 3	√15 = 3.87
   3d⁸	5 singles, 3 paired: n = 2	√8 = 2.83
   3d³	3 singles: n = 3	√15 = 3.87
   3d⁶	5 singles, 1 paired: n = 4	√24 = 4.90

3. So. [Ar] 3d⁶ has the most unpaired electrons, 4, and so the highest magnetic moment, about 4.90 BM. The answer is (d).

The idea to keep. For dⁿ, unpaired electrons are n up to d⁵ and 10 - n after it. Compare those counts, not the total number of d electrons.

Answer from the NTA final answer key. Solution by PrepWiser.