Although the spin angular momentum of an electron is "' ", the intrinsic magnetic moment of the electron caused by its spin is still approximately one Bohr magneton.
12.
The magnetic dipole moment of the electron, which is much larger as a consequence of much larger charge-to-mass ratio, is usually expressed in units of the Bohr magneton.
13.
Where is the exchange energy, the operators represent the Land?factor, is the Bohr magneton and is the internal field which includes the external field plus any " molecular " field.
14.
This is the basis for defining the magnetic moment units of Bohr magneton ( assuming charge-to-mass ratio of the electron ) and nuclear magneton ( assuming charge-to-mass ratio of the proton ).
15.
It is essentially a proportionality constant that relates the observed magnetic moment " ? " of a particle to its angular momentum quantum number and a unit of magnetic moment, usually the Bohr magneton or nuclear magneton.
16.
The angular momentum of an electron is either + | 2 } } or " | 2 } } due to it having a spin of, which gives a specific size of magnetic moment to the electron; the Bohr magneton.
17.
Where \ boldsymbol { S } is the spin angular momentum vector, \ mu _ \ text { B } is the Bohr magneton and g _ \ text { s } \ approx 2 is the electron spin spin, so the magnetic moment is antiparallel to the spin angular momentum.
18.
Where N is the number of magnetic atoms ( or molecules ) per unit volume, g is the Land?g-factor, \ mu _ B ( 9.27400915e-24 J / T or A�m 2 ) is the Bohr magneton, J is the angular momentum quantum number and k _ B is Boltzmann's constant.
19.
The constant A is known as the zero field hyperfine constant and is given in units of Hertz . \ mu _ B is the Bohr magneton . \ hbar \ vec J and \ hbar \ vec I are the electron and nuclear angular momentum operators . g _ J and g _ F can be found via a classical vector coupling model or a more detailed quantum mechanical calculation to be:
20.
The term symbol for the ground state of atomic iron is 5 D 4, so the quantum numbers are S = 2, L = 2, and J = 4 . ( S is what's usually called " the spin ", because it involves only the intrinsic spins of the electrons, but J is the total angular momentum . ) By my calculations, that makes the Land?g-factor equal to 3 / 2, so the total magnetic moment is 4 * 3 / 2 = 6 Bohr magnetons.
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