SE-9654
Zeeman Effect Experiment
34
012-14266B
Questions:
1. Do the “Mean” values for the Bohr magneton,
Bohr and
B, from Table 2 and Table 3 agree with theory (9.27 x 10
-24
J/
T)? Discuss fully.
The values are close. The k = 0 mean value is about 3% low and the k = 1 mean value is about 2% low. Based on the stan-
dard deviation of the three runs, the precision is about 2.5% for the k = 1 values but less than 0.5% for the k = 0 values.
This is probably optimistic for the k = 0 data since the calculation is based on (R
+
²-R
-
²) = (R
+
-R
-
)(R
+
+R
-
) x
R. Note that
R is about ± 2% for the k = 1 case in good agreement with our result, but
R is about ± 1% for the k = 0 case so the
uncertainty in µ Bohr cannot be less than 1% and there was some luck involved in getting three value that agree within
0.4%. Thus, the k = 0 and k = 1 values agree with each other. However, since the k = 0 value has an uncertainty that is
about 2.5 times smaller, when we average the values, we should weight the k = 0 value 2.5² = 6 times heavier. So we have
µ Bohr = 9.02(10) x 10
-24
J/T. This does not quite agree with the theory value and we note that almost all the values are
low. This implies a small systematic error. Direct measurement shows that the field in the gap between the poles is some-
what low in the region near where the axial hole was drilled, even with the plug in place. This would explain our slightly
low result. Nevertheless, the results are impressive.
2. When the current was on, was the center Radius Tool circle in the triplet the same as the Radius Tool circle for the B = 0
field? What does this show?
Yes, the center circle of the triplet was the same as B = 0 line. This means that the energy of the center line does not shift.
•
On the “Data Analysis” workbook page, select Run #2 at the bottom of the page. Move the playback slider to the begin-
ning of the run (all the way to the left). Using the “Create Measurement Tool” button, create three Radius Tools. Adjust
one of the circles so it is just outside of the outer k = 1 triplet. Adjust a second circle to just inside the inner k = 1 triplet.
Adjust the third circle to just outside the k = 0 triplet. Move the slider until the k = 1 triplet disappears.
3. How many energy levels do you see now for the k = 1 band of circles? Does this agree with the discussion in the theory
section?
With the polarizer perpendicular to the field axis, there are three levels above where the triplet levels were and three levels
below. This is exactly what was predicted.
•
Now move the playback slider to the end of Run #2 where the polarizer was removed.
4. Can you see all the bands? How many are there? Does it match theory?
Now nine level show. This agrees with prediction.
•
Now select Run #3 at the bottom showing the interference pattern for the axial magnetic field (when the electromagnet
was parallel to the track). Start with the slider at the beginning and move it to the end. Recall that you rotated the polarizer
through 90° as you took the movie.
5. Do you see any change in the pattern? What does this tell you?
Rotating the polarizer has no affect on the pattern. This shows that the light is either unpolarized or circularly polarized.
(It is actually circularly polarized.) With circular polarization, the axis of polarization rotates. This means that every half
cycle the light gets through independent of the polarizers orientation. Since the rotation is very fast, we see only the aver-
age which is independent of polarizer orientation.
6. Why is all of this important?
This is direct evidence that the magnetic moment of atoms in quantized both in magnitude and (more surprisingly) in
direction. Although most students have accepted this by believing in the quantum numbers taught in a basic chemistry
class to explain the atomic table (which they do quite well), here we see direct evidence of the quantization. To classical
physicists educated before 1920, this idea was astonishing!