Magnetic Properties and the Spin-Only Formula

Find oxidation state, write the ion configuration, remove ns electrons first, fill d-orbitals according to Hund's rule for the expected case, count unpaired electrons, and substitute n in sqrt(n(n+2)) BM.

An orbital box diagram is useful for counting unpaired electrons, especially for d1 to d10 configurations.

A common wrong answer is using n as oxidation number instead of number of unpaired electrons, leading to a wrong magnetic moment.

Magnetic behaviour of transition-metal ions depends mainly on the number of unpaired electrons. Paramagnetic species have unpaired electrons, while diamagnetic species have all electrons paired.

Magnetic behaviour of transition-metal ions depends mainly on the number of unpaired electrons. Paramagnetic species have unpaired electrons, while diamagnetic species have all electrons paired. Spin-only formula: magnetic moment = sqrt(n(n+2)) BM, where n is the number of unpaired electrons and BM means Bohr magneton. Paramagnetic: n greater than 0; diamagnetic: n = 0. Mn₂⁺ has 3d5 configuration with five unpaired electrons. Its spin-only magnetic moment is sqrt(5(5+2)) = sqrt(35) = about 5.92 BM.

Unpaired electrons behave like tiny magnetic centres because each electron has spin. In transition-metal ions, the number of unpaired d-electrons is therefore the main school-level reason for paramagnetism. The spin-only magnetic moment uses only spin contribution and ignores orbital contribution, which is a reasonable approximation for many first transition-series ions in CBSE problems. A species with n = 0 is diamagnetic and has no spin-only magnetic moment, while species with larger n values are more strongly paramagnetic. Correct counting must be done for the ion, not the neutral atom, because cations lose ns electrons before (n-1)d electrons. Spin-only formula: magnetic moment = sqrt(n(n+2)) BM, where n is the number of unpaired electrons and BM means Bohr magneton. Paramagnetic: n greater than 0; diamagnetic: n = 0. Find the magnetic moment of Fe₃⁺. Fe has atomic number 26; Fe₃⁺ is [Ar] 3d5 after removing two 4s electrons and one 3d electron. Five unpaired electrons give magnetic moment = sqrt(5(7)) = sqrt(35) = about 5.92 BM. Questions may ask for magnetic moment, number of unpaired electrons, comparison of magnetic strength, or identification of para- and diamagnetic ions. A common wrong answer is using n as oxidation number instead of number of unpaired electrons, leading to a wrong magnetic moment.