Question

Formula to calculate spin only magnetic moment

Answer 1

The formula used to calculate the spin-only magnetic moment can be written in two forms; the first based on the number of unpaired electrons, n, and the second based on the total electron spin quantum number, S. Since for each unpaired electron, n=1 and S=1/2 then the two formulae are clearly related and the answer obtained must be identical.

μso= √n(n+2) B.M.

μso= √4S(S+1) B.M. - a variation of this will be introduced in the
second year Inorganic course: μS+L = √{4S(S+1) + L(L+1)} B.M.

Answer 2

$\mathbb{ \ \ ANSWER \: \: }$

The total spin momentum has magnitude Square root of√S(S + 1) (ℏ), in which S is an integer or half an odd integer, depending on whether the number of electrons is even or odd.