Zeeman Effect Experiment
Final Theory
9
012-14266B
By measuring the R values in the B = 0 pattern, the constant C
0
can be determined to better than 0.5%.
With an applied magnetic field, through a polarizer parallel to the magnetic
field, the spectral lines each split into three lines. The center line in each trip-
let has the same wavelength as for the B = 0 case. The inner ring with radius
R
k-
has a slightly longer wavelength and the outer ring (R
k+
) has a slightly
shorter wavelength. Equation 10 is still valid and yields the following:
and
Subtraction yields:
Using Equation 7 and the excellent approximation (n - k)
= n
= 2d yields:
where h is Planck’s constant and c is the speed of light. Solving for the Bohr magneton,
B
, yields:
where C
0
is the constant determined previously (Equation 12) and d = 1.995 mm is given for the separation of the Fabry-Perot
parallel plates (called the ‘etalon’).
2
2
0
2
0
2
2
2
0
1
Eqn. 12
k
k
d
R
R
k
f
d
k
C
f
R
R
Figure 5: B
0 Pattern, Triplets
R
1
R
1+
R
1-
where k = 0, 1, 2, 3...
2
k
2
R
2d 1
n k
2f
where k = 0, 1, 2, 3...
2
k
2
R
2d 1
n k
2f
where k = 0, 1, 2, 3...
2
2
k
k
2
d
R
R
n k
f
2
2
2
B
B
k
k
2
B
B
2d
d
R
R
n k
hc
hc
f
where k = 0, 1, 2, 3... Eqn. 13
2
2
0
B
k
k
C hc
R
R
2dB