For a metal ion, the calculated magnetic moment is 4.90 BM. This metal ion has ___________ number of unpaired electrons.

Solution

Chemistry ma’am · 3 steps

Use the spin-only formula and test small values of n until the root gives 4.90.

1. Spin-only formula. For d-block ions the magnetic moment comes almost entirely from the unpaired electrons. With n unpaired electrons, the moment in Bohr magnetons is given by the formula below.

   μ = √n(n+2) BM

2. Square both sides. 4.90² = 24.01, so n(n+2) ≈ 24. Try n = 4: 4 × 6 = 24, which fits exactly.

   Unpaired electrons n	n(n+2)	μ (BM)
   2	8	2.83
   3	15	3.87
   4	24	4.90
   5	35	5.92

3. So. A moment of 4.90 BM means the ion has 4 unpaired electrons.

The common slip: 5. Using μ = √n(n+1), the formula with the wrong added term, makes n(n+1) = 24 and pushes you to about 4.4, so some round to 5 instead of 4.

The idea to keep. Learn the spin-only ladder by heart: 1.73, 2.83, 3.87, 4.90, 5.92 BM for 1 to 5 unpaired electrons. Then any moment tells you n at a glance.

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