Paramagnetic substances are attracted by an external magnetic field, that is, they move from a weaker to a stronger part of the field. Paramagnetic substances contain unpaired electrons. Diamagnetic substances are repelled by an external magnetic field, that is, they tend to move away from the stronger part to the weaker part of the field. In diamagnetic substances, all the electrons are paired.
The magnetic moment of a substance arises from the spin angular momentum and the orbital angular momentum of its electrons. In many compounds of the 3d series metals, the orbital contribution is neglected, because the orbital motion of these electrons is quenched by the surrounding species in the compound or solution. The magnetic moment is then calculated by the spin-only formula, in Bohr magnetons (BM):
\[\mu_s = \sqrt{n(n + 2)}\ \text{BM}\]
where n is the number of unpaired electrons.
The magnetic moment of an ion in its +3 oxidation state is 3.85 BM. The number of unpaired electrons in it is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3
For ions of the 3d series the orbital contribution is quenched, so the magnetic moment depends only on the number of unpaired electrons n, through the spin-only formula:
\( \displaystyle \mu_s=\sqrt{n(n+2)}\ \mathrm{BM} \)
Squaring both sides with μs = 3.85 BM:
\( \displaystyle n(n+2)=(3.85)^2=14.8\approx 15 \)
\( \displaystyle n=3,\ \text{since}\ 3\times(3+2)=15 \)
Check: \( \sqrt{15}=3.87\ \mathrm{BM} \), which matches the given 3.85 BM. The ion has 3 unpaired electrons; the +3 charge does not change the calculation.