bei48482_FM

(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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