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6.4 Measurement of hyperfine structure 115

Beam source

Collimator

Atoms deposited in two places

Magnet

Fig. 6.13In the original Stern–Gerlach

apparatus a beam of silver atoms was

sent through a region of strong gradi-

ent of the magnetic field and further

downstream the atoms were deposited

on a glass plate. This simple experi-

ment had a great influence on the devel-

opment of quantum ideas and provides

a very useful illustration of the concepts

of quantisation (Feynmanet al.1963–

1965).

that are half-integer multiples of
. (Orbital angular momentum would
give 2l+ 1 components, withlan integer.) To interpret the experiment
we consider an atom in a magnetic fieldBwith a gradient along the
z-axis.^36 The force exerted on the atom is (using eqn 5.11)^36 Since∇·B= 0 we cannot have a
gradient along thez-axis without there
also being a gradient in another direc-
tion, but the effect of a gradient in a di-
rection perpendicular toBaverages to
zero as the magnetic moment precesses
around thez-axis—for a more rigorous
discussion see Chapter 10.

Force =−

dEZE

dz

=gJμB

dB

dz

MJ. (6.39)

The ground level of silver, 5s^2 S 1 / 2 ,hasl=0andJ=s=1/2. Thus
the force on atoms passing through the Stern–Gerlach magnet has the
two valuesF =±μBdB/dzforms=MJ =±^12. This explains the
separation of the atomic beam into two components and provides direct
observational evidence for quantisation since the two emerging beams are
well defined. For a classical vector thez-component of angular momen-
tum would be spread over a range between the maximum and minimum
values.
An atomic-beam apparatus has two Stern–Gerlach-type magnets, as
shown in Fig. 6.14, that create an inhomogeneous field in the A and B
regions to deflect atoms according to theirMJstate. The A and B re-
gions have a strong field (μBBA), associated with the high gradient
of magnetic field there, soMJis a good quantum number and eqn 6.39
gives the force. The transition to be measured occurs in the C region
between the two state-selecting magnets where, generally, the atoms
are in the low-field regime. The principles of the operation of such an