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SE-9654
Zeeman Effect Experiment
6
012-14266B
Figure 1 is not to scale. The splitting between the 2J + 1 levels is much less (~10
-5
) than the splitting between the original two
levels.
In the diagram, M
Z
is the projection of the orbital angular momentum on the z axis. Selection rules allow transitions between
states where
M
Z
= +1, 0, -1. The transitions where
M
Z
= 0 produce photons that are polarized parallel to the magnetic field
axis and the spectral lines are more intense. These are the lines that will be used for measurement. The
M
Z
= +1, -1 transi-
tions produce photons polarized perpendicular to the field axis. Using a polarizer to eliminate the
M
Z
= +1, -1 lines makes it
easier to do measurements.
Let E
S
be the energy of the un-split (B = 0)
3
S
1
state. This is exactly equal to the M
Z
= 0 energy level when the field is not
zero. Let
E
S
be the shift in energy from the M
Z
= 0 S state when B
0. Similarly for E
P
and
E
P
. The energy shift is deter-
mined by the component of the magnetic moment of the atom along the magnetic field and is given by Equation 1:
where g
L
is the Landé g factor and
B
is the Bohr magneton. Recall that the Bohr magneton is the elemental unit of magnetic
moment (analogous to electron charge, e, being the elemental unit of electric charge). All atomic magnetic moments are inte-
ger or half-integer multiples of
B
, the Bohr magneton. The Bohr magneton is the classical magnetic moment that an electron
in the first Bohr orbit of hydrogen would posses. Such an electron may be treated as a tiny current loop with current:
where T is the time for one orbit of the electron, v is the speed of the electron in the first Bohr orbit, m is the electron mass, and
r
B
is the Bohr radius. The magnetic moment of a single current loop is given by Equation 2:
Figure 1: Energy Levels for 546.1 nm Mercury Spectral Line
E
M
Z
g
L
B
B
Eqn. 1
=
i
e
T
----
e
2
r
B
v
-------------
------------------
ev
2
r
B
-------------
e
2
r
B
-------------
h
2
r
B
m
------------------
eh
m 2
r
B
2
-------------------------
=
=
=
=
=
B
iA
r
B
2
eh
m 2
r
B
2
-------------------------
eh
4
m
------------
9.274x10
24
–
J T
Eqn. 2
=
=
=
=