Unpaired electrons from a magnetic moment

Worked example

A transition-metal complex has an effective magnetic moment of 4.97 Bohr magnetons. Assuming a spin-only moment, how many unpaired electrons does it have?

1. 1. Spin-only magnetic moment: solve for Unpaired electrons

   $n = \sqrt{1 + \mu^2} - 1$

   = 4.070

Answer: n (unpaired) = 4.07

Method

μ = √(n(n+2)) gives n = √(1 + μ²) − 1; round to the nearest whole number. Spin-only values are 1.73, 2.83, 3.87, 4.90 and 5.92 μB for 1–5 unpaired electrons; real complexes differ slightly because of orbital contributions.

Formulas used

• Spin-only magnetic moment

  $\mu_\text{so} = \sqrt{n(n+2)}\;\mu_\mathrm{B}$

More spectroscopy & other questions

• Concentration from absorbance
• Wavelength to break a bond
• Density of a rock-salt crystal
• Atomic radius of a face-centred cubic metal
• Atomic radius of a body-centred cubic metal
• Crystal field splitting from a d–d absorption