Free electron energy levels

An unpaired electron in a molecular radical can be considered to be an effectively free electron. A free electron in a magnetic field has two energy levels due to the two possible orientations of
its spin, and hence of its magnetic moment, with respect to the magnetic field.
The energies of the levels are given by:

E = -μs.B = +- μB.B , where 

If an oscillator of frequency 50 MHz is used for an ESR experiment, we can easily calculate the magnetic field required to achieve a transition:

hf = 2μB.B, rearranging this gives us: B = hf*meC/(e*hbar) = 2*f*pi*meC/e
using f = 50 MHz, we get get B = 1.78 mT


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