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Zeeman Effect Experiment
Theory
7
012-14266B
where A is the area of the current loop. Note that this derivation is not quantum mechanically correct and gives the wrong
value for the first Bohr orbit of hydrogen, but the value for the Bohr magneton is correct.
The Landé g factor is:
For both states, the two valence electrons couple to give S = 1. Then L = 0 for an S state and L = 1 for a P state. The total angu-
lar momentum is J = 1 for the S state and J = 3 for the P state. This gives:
g
S
=
2
(for
3
S
1
) and
g
P
=
3/2
(for
3
P
2
)
Equation 1 then yields Equation 3:
where M
Z
= ±1 for the states of interest.
Looking at the
M
Z
= 0 transitions, the M
Z
= 0 to M
Z
= 0 transition will result in the same
= 546.1 nm wavelength as the
B = 0 case. For the M
Z
= +1 to M
Z
= +1 transition,
h
+
= (
E
S
+
E
S
) - (
E
P
+
E
P
)
Eqn. 4
For the M
Z
= -1 to M
Z
= -1 transition,
h
-
= (
E
S
-
E
S
) - (
E
P
-
E
P
)
Eqn. 5
Subtracting the two equations and using Equation 3 yields:
h(
+
-
-
) = 2(
E
S
-
E
P
) =
B
B
Eqn. 6
Converting to wavelengths:
where (
-
)(
+
) =
2
to extremely good approximation.
Fabry-Perot Interferometer
The interferometer consists of two partially reflective optically flat plates
of glass (called the elaton) that are parallel to a high degree of accuracy.
The spacing between the plates of glass, d, is 1.995 millimeters (mm).
The collimating lens causes rays of light that originate on the optical axis
to come in parallel to the optical axis. However, the source is not a point
source and rays that originate on the source at a position that is at a small
angle,
, from the optical axis seen from the collimating lens will reach
the interferometer nearly parallel and at the same angle
from the optical
axis as shown in Figure 2.
Ray 1 is partially reflected at points A and B (the transmitted rays are not
shown). It then interferes with Ray 2, since they both follow the same
path after point B. Ray 1 travels along a path that is longer than Ray 2 by:
g
L
1
J J 1
+
S S 1
+
L L 1
+
–
+
2J J 1
+
----------------------------------------------------------------------------
+
=
E
S
2B
B
and
E
P
3 2
B
B
Eqn. 3
=
=
2
2
B
B
hc
hc
c
c
h
B
B
Eqn. 7
hc
Figure 2: Fabry-Perot Geometry