The formula for calculating spin-only magnetic moment is given by μ=√n(n+2) where n is the number of unpaired electrons.
To determine the number of unpaired electrons in a complex, you need to first determine the electronic configuration of the central metal ion. Then, using Hund's rule, fill up the orbitals with electrons, taking into account any ligand field splitting. The number of electrons in the partially filled orbitals is equal to the number of unpaired electrons in the complex.
The electronic configuration of Fe(III) is [Ar]3d5. This means that there are 5 electrons in the d-orbitals, with 3 pairs and 1 unpaired electron.
Ligand field splitting affects the spin-only magnetic moment by reducing the number of unpaired electrons. This is because the ligand field can cause some of the electrons to pair up, resulting in a lower magnetic moment.
The spin-only magnetic moment for [Fe(H2O)5NO](2+) is calculated by first determining the number of unpaired electrons. In this case, Fe(III) has one unpaired electron, so the magnetic moment is equal to √1(1+2)=√3μB.