(a)
μ = IA
(b)
μ = –( 2 em)L
μ
B
L
- e
v
μ
I
B Area = A
Figure 6.16(a) Magnetic moment of a current loop enclosing area A. (b) Magnetic moment of an
orbiting electron of angular momentum L.
for an orbital electron (Fig. 6.16). The quantity (e 2 m), which involves only the
charge and mass of the electron, is called its gyromagnetic ratio.The minus sign means
that is in the opposite direction to Land is a consequence of the negative charge of
the electron. While the above expression for the magnetic moment of an orbital electron
has been obtained by a classical calculation, quantum mechanics yields the same result.
The magnetic potential energy of an atom in a magnetic field is therefore
UmLB cos (6.40)
which depends on both Band .
Magnetic Energy
From Fig. 6.4 we see that the angle between Land the zdirection can have only the
values specified by
cos
with the permitted values of Lspecified by
Ll(l 1 )
To find the magnetic energy that an atom of magnetic quantum number mlhas when it is
in a magnetic field B,we put the above expressions for cos and Lin Eq. (6.40) to give
Magnetic energy Umml B (6.41)
The quantity e 2 mis called the Bohr magneton:
(^) B9.274 10 ^24 J/T5.788 10 ^5 eV/T (6.42)
In a magnetic field, then, the energy of a particular atomic state depends on the value
of mlas well as on that of n. A state of total quantum number nbreaks up into several
substates when the atom is in a magnetic field, and their energies are slightly more or
slightly less than the energy of the state in the absence of the field. This phenomenon
e
2 m
Bohr
magneton
e
2 m
ml
l(l 1 )
e
2 m
224 Chapter Six
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