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Zeeman Experiment: General Procedures and Cautions
Background: The quantum and classical physics predictions of the shifts of atomic
energy levels due to the interaction with a magnetic field differ qualitatively and
quantitatively. Classical mechanics and electrodynamics predict that an applied magnet
field that should split an atom’s levels and hence spectral lines into three components
when viewed along a line perpendicular to the field.1 The light observed with polarization
parallel to the field should have the zero-field frequency while the components polarized
perpendicular to the field should have frequencies shifted by BBh-1 where B is the
Bohr magneton. Lines that split in this fashion are said to exhibit a Normal Zeeman
Effect. Quantum Mechanics makes rather more complicated predictions. The 405 nm line
of mercury is predicted to split into three components as predicted above, but with
component to component separations of 2BB. The green line is predicted to split into
nine components with separations of ½BB. Other patterns are discussed in the mercury
spectrum section. Any departure from the classical pattern in the number of components
or the magnitudes of the splitting is an example of an Anomalous Zeeman Effect. We
will only observe anomalous cases.2 The results are important because classical physics
e
predicts that an electron’s magnetic moment should be – 2me multiplied by its angular
momentum; quantum mechanics boldly predicts about twice this value. Experimental
values for B (=
e
2 me )
are needed to make the comparison to verify that quantum rules.
Observations of anomalous behavior supported the new quantum theory early in its
development.
http://www.youtube.com/watch?v=4S0_77PwaGg
Different free spectral range 7 or 9 components? See page 15
1
See Appendix VII: The classical theory of the Normal Zeeman Effect or The Physics of Atoms and Quanta: Introduction to
Experiments and Theory by Hermann Haken, Hans Christoph. Wolf, William D. Brewer, p.210ff.
2
The cadmium red line displays a normal Zeeman Effect (Quantum and classical agree in this case.). A
filter and lamp to observe that line would cost about $1300.
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
Lab Report Content:
Experiment I: Green Line Zeeman Deliverables:
A report on the green line Zeeman should include.
A zero field calibration image. Your pixel to frequency calibration equation.
A set of images for the lines (polarized vertically) for the four field strengths3
A set of images for the lines (polarized horizontally) for the four field strengths
An experimental value of B assuming a 2.04 B B model separation of the + and - peaks.
Estimates of the full width at half maximum (FWHM) of the collection of lines for the four
field strengths. Compare that to a model of that width using a single component FWHM of 9
GHz and a component to component separation of ½ h-1B B.
Experiment II: Yellow Line Zeeman Deliverables:
A zero field calibration image. Your pixel to frequency calibration equation.
Images with both 577 and 579 nm lines.
A set of images for the lines (polarized vertically) for the four field strengths4
A set of images for the lines (polarized horizontally) for the four field strengths
Images with the 577 lines only. You must recalibrate!
WARNING: The mercury lamp emits significant amounts of UV radiation. Do not view
the lamp directly. Any optic including a lens in a pair of glasses will effectively block the
harmful radiation.
Mercury Lamp: Turn on the lamp by pressing the left button on the power supply in the
base of the magnet. The black knob should be rotated fully CCW, and the right button
should be off (dark). Leave the lamp on until you are through taking data. Do not cycle
the lamp unnecessarily.
3
4
Zero is a field strength.
Zero is a field strength.
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
B Field Measurement: Use the Tri-Field Meter to measure the field as a function of the
current as indicated by the ammeter on the power supply. Set the current to correspond
to convenient reference lines on the ammeter face that correspond to magnetic fields of
about 0, 1/3 Bmax, 2/3 Bmax and Bmax. (Try for four separated values of B running from 0 to
Bmax. Off or zero field; On at lowest value; One at a marked mid range value; full On)
Tri-Field Gaussmeter: Use the peak hold feature to find the
maximum field strength for each current. Disengage the
peak hold feature and move the probe around to estimate the
homogeneity of the field. As an example, if you estimate
that the field is between Bmax and 0.94 Bmax over the several
cubic mm of the lamp from which radiation is being
observed, the individual lines will be smeared by 3%
about line center. TURN CURRENT OFF WHEN NOT IN USE.
NOTE: It is necessary to turn on the mercury lamp in order to energize the magnet.
Remove the lamp with its connecting wires from the clamp holding it between the
pole pieces and set it down gently near the base of the magnet. Make peak-hold
measurements of the magnetic field strength for your measurement current values.
After the measurement gentlty re-insert the lamp in its holder between the pole pieces.
The Camera: See page 13.
Open the panel on the left side exposing the CCD monitor window on the camera.
Check to see that the shutter is open. --- Front right side of camera.
Be sure that the power cord is attached at the top rear of the camera and that video out
cable is securely inserted in the jack located near the lower rear of the camera on the side
with the CCD display.
Leave the camera settings as you found them otherwise unless the image appears to be
saturated. If so, read the section the instruction for resetting the shutter speed. Set it to get
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
largest exposure time for which no saturation occurs. Do not charge or move the camera
after the calibration image is captured.
The video capture card used in prior years with the Zeeman experiment has been replaced
by a USB interfaced capture device hosted by the Pinnacle Studio software. The next
page presents a method to use this device to capture still images. Please suggest
modifications to this section and to any other section that might improve the
experience. Beware, most of this guide still assumes that the old PCI capture card is
being used.
Find the data storage folder using the Zeeman Data shortcut on the desktop. Create a new
folder at the location for your group’s data.
Launch Pinnacle Studio - it opens about as slowly as any software you have seen.
The software supports several video formats. Whenever you are presented with the
option: Select COMPOSITE. Composite video combines all three colors in a single
composite signal. Avoid RGB or S video.
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Zeeman Experiment: General Procedures and Cautions
http://www.steves-digicams.com/knowledge-center/how-tos/photosoftware/pinnacle-studio-how-to-set-up-the-capture-format-settings.html
ImageJ formats: Save files in a format compatible with ImageJ.
http://imagejdocu.tudor.lu/doku.php?id=faq:general:which_file_formats_are_suppo
rted_by_imagej
Select Import
Stop Motion
CaptureFrames @ 8 f.p.s.
Frames 1 to 8 will be 00.00, 00.01, … , 00.07
Frames 9 to 16 will be 01.00, 01.01, … , 01.07
……..
To begin, set the experimental conditions and then capture 8 frames.
Click Start Import.
StopMotion ….. . AVI appears on the Pinnacle work space. Drag the stop motion file
onto the first empty position on the film strips along the lower edge of the window. Click
on that film position to select it.
Select Grab Frame from the Toolbox menu
Click Grab Frame, Save to Disk. Name as Conditions…1.
I use the Bitmap (.BMP) format, but others are allowed.
Go to small display window in the upper left area. Use the little arrows to advance one
frame. Click Grab Frame, Save to Disk. Default name will appear as Conditions…2.
Repeat for the additional frames.
Adjust the experimental conditions and repeat the process beginning with a filename like
NewConditions…1 and so on. Repeat for the additional sets of experimental conditions.
Copy all the files to your thumb drive or a server.
The images are to analyzed using the ImageJ software.
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
You must keep each image as originally captured. Also save images modified by
adjusting the image color balance using ImageJ.
Menu: Image Adjust Color balance
The detailed instructions for the color adjustment are in Appendix II.
Email the captured images to your account. Download ImageJ from:
http://rsbweb.nih.gov/ij/ for use on your computer. It is freeware!
Alignment: (see Appendix I)
CAUTION: You must never touch an optical surface. Never touch the mirrors in
the etalon, the surfaces of the filter, of any lens or of the polarizer. Take the time to
study the physical layout of the components before you tighten or loosen the etalon
alignment screws or rotate the polarizer so that you can avoid touching the optical
surfaces. THIS IS IMPORTANT. Do not attempt to clean an optical surface; inform
your instructor when surfaces require cleaning.
Remove the camera and observe the green ring pattern. If the rings breathe (grow and
contract) as you move your line of sight left and right and up and down, the alignment
needs to be refined. There are three alignment screws on the face of the etalon nearest to
the magnet. Tighten and loosen each screw in turn as you move your head back and forth
along a line perpendicular to the line joining the other two screws. (Tighten and loosen;
do not just tighten!! Use finger tightness only. Do not use tools to tighten the screws as
catastrophic damage may result if screws are over tightened. Read the alignment
appendix for more details.) When you no longer observe the rings growing and
contracting, move on to the next step.
B = 9.274 x 10-24 J/T.
h = 6.626 x 10-34 Js
B
h
14.33 GHz T
The 546 nm radiation from mercury has an approximate frequency of 5.5 x 1014 Hz. This
green line splits into nine components with component to component frequency
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
differences of ½BBh-1 or about 7.7 GHz in the maximum magnetic field 5. We need a
resolving power, f/f , of 800,000. Unfortunately, our etalon does not provide this level of
performance so we will observe groups of lines separated by more than 14 GHz, a
difference that the etalon can resolve.
The Green Line Data: Observe the pattern with the green pass filter in place and the
magnetic field turned off. Get a good image with the center of the ring pattern a little to
the right (or left) of the center of the video image and at its half height. Turn on the B
field on and watch the rings increase in width. The ring pattern is actually nine rings
equally spaced (by ½BB) that are not resolved.
The 7 GHz component to component spacing is smaller than can be resolved using the
apparatus as configured. It is hoped that the system performance will be improved over the
term to the point that lines separated by 7 GHz will be just barely resolved. Stay tuned.
Rotate the polarizer to block the horizontally polarized lines in each of the wide rings
revealing each ring apparently split into two rings. The two ‘rings’ are each a set of three
line components that are polarized vertically as viewed.
5
Energy level differences are given in energy, frequency or perhaps even wavelength units. Modern physics student should
multiply by factors of h and c are necessary.
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
3
E0 ( S1 ) 2 B Bext
3
E0 ( S1 )
3
E0 ( S1 ) 2 B Bext
3
S1
g=2
mJ = -1, 0, 1
E E0 (3 S1 ) E0 (3 P2 ) B Bext
2 to 2 by ½
3
E0 (3 P2 ) 3 B Bext
E0 (3 P2 ) 3 2 B Bext
P2
g = 3/2;
E0 (3 P2 )
E0 ( P2 ) 2 B Bext
E0 (3 P2 ) 3 B Bext
3
3
mJ = -2, …. , 2
Quantum Mechanics Predicts:
Upper: 3S1 gu = 2
Mercury Green: 546.07 nm
Landé g Factor
g 1
Lower: 3P2 g = 3/2
J ( J 1) L( L 1) S ( S 1)
2 J ( J 1)
;
E = Eo + g mJ
As viewed along a direction perpendicular to the field, the components polarized parallel
to the field are labeled as lines and correspond to transitions for which mj = 0. The
components polarized perpendicular to the field as labeled as lines and correspond to
transitions for which mj = .
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
Figure 1: The lines are horizontally polarized (as
viewed), and the lines are vertically polarized. Due to
the contributions from the smaller outer components, the
peak to peak separation between the unresolved
components is just greater than 2.0 B B. The relative
intensities of the components are 1:3:6:6:8:6:6:3:1.
Poorly resolved pattern:
{
pol B
{
{
pol B
pol B
2.04 BB
1:3:6:6:8:6:6:3:1
4 B B
2+ B B
1:3:6
6:3:1
line polarization blocked
Model of intensity vs. energy in units of ½ BB.
The to ring peak separation is modeled as 2.04 BB.
The point is that we can resolve lines split by 2 B B so we can take data.
Survey the problem. Remove the camera and set the B field to its maximum. View the
image as you rotate the polarizer. The optic nearest the magnet has a collimating lens on
the magnet side and a linear polarizer that can be rotated on the camera side. An
imaginary line from the center to the red dot indicates the linear polarization passed by
the polarizer. View the pattern as you rotate the polarizer. Set the polarizer to pass the
horizontal polarization; observe the pattern as you vary the field strength. Set the
polarizer to pass the horizontal polarization; observe the pattern as you vary the field
strength. Set the polarizer at 45o; observe the pattern as you vary the field strength.
Record your qualitative observations. Set the polarizer to pass the vertical polarization
and continue.
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
Turn the field down to zero. Without changing anything related to the optical setup6,
capture several images for field strengths of 0, BonLow, BonMed and Bmax7 with the polarizer
set to pass the vertically polarized lines only, the horizontally polarized lines only
and all the lines (polarizer set 450 in between the previous two orientation. Use the zerofield image to develop a frequency calibration of the image for the given fixed optical
configuration. See the position (vs. frequency) calibration Appendix V. SAVE images in
JPEG format. (BMP and other are supported by the Dazzle capture device.)
Zero Field Image opened in ImageJ.
For a calibration image that crosses
the center, assign frequencies
symmetrically in multiples of the free
spectral range, 75 GHZ. Do not
Fig. 2: A zero field ring pattern with a plot profile generated in ImageJ.
assign 0 to the center as it has v
This profile was obtained using a research grade Fabry-Perot.
offset.
Note that the central bright spot shows saturation – intensity > level 255
(0 to 28-1) supported
Open the zero field image in ImageJ. Apply the image color balance procedure in that
appendix before further analysis. Retain copies of the original images. Find the
horizontal position x (expressed in pixels) for each frequency peak. The innermost ring is
defined to be the 75 GHz ring and each ring outward has a frequency that is incremented
by + 75 GHz, the free spectral range of an etalon with plate to plate spacing of 2 mm.
Select a thin horizontal slice that runs almost the full width across the image. The image
below identifies x = 477 pixels from the left edge for the 150 GHz peak. The current
camera has 640 horizontal pixels.
6
7
Any change of optical setup invalidates the pixel to frequency calibration.
You must measure the field strength for each of these settings. A gaussmeter is provided.
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
*** Be sure that the arrow keys are used to move the data rectangle against the left
edge of the image. Do this consistently. Under the Analyze menu choose Plot Profile.
Define a thin rectangle of data as illustrated; it should run from the left edge to almost the
right edge. Under the Analyze menu, choose Measure to enable a cursor to select points
on the curve. The x and y values are displayed for the point currently marked by the
cursor. The x data is the position of each peak in pixels and the ordinate value is the
frequency assigned to that peak.
The sample data below was obtained using a research grade etalon. The peaks in your
image will not be as sharp. A complete data set would be of the form:
Table 1. (Imaginary data set; Not for the image below.)
x
f(x)
75 GHz
150 GHz
225 GHz
300 GHz
f(x) = (384.319 - 0.604853 x + 0.000238966 x2) GHz
= (1.58 + 2.39 x 10-4 (x – 1266)2) GHz
375 GHz
x: pixel number
alternate form of equation above
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
Calibration: Fit the data to f(x) = fo + a x + b x2 using a quadratic fit procedure. Indentify
the parameters fo, a and b. Try to find a procedure that also provides uncertainty estimates
for the parameters. See the fitting section.
The calibration must be repeated if any optic other than the polarizer is adjusted. See
the position calibration section for more details.
Composite Image: The zero field ring pattern is shown in the upper half. The lower half
displays the ring pattern for the vertical polarization in a field of about one Tesla. The
two groups of three sigma components are shifted in opposite senses leaving a void at the
zero field ring position. The zero field ring8 at 75 GHz splits into two rings at positions
that the calibration identifies as 84 GHz and 67 GHz corresponding to a peak to peak
splitting of 17 GHz. The zero field ring at 150 GHz splits into two rings at positions that
the calibration identifies as 159 GHz and 141 GHz corresponding to a peak to peak
8
This experimenter failed to label the innermost ring as the 75 GHz ring. Add 75 GHz to each frequency in the image.
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
splitting of 18 GHz. (Note we could perhaps add positive shift data for the 225 GHz ring
and if we called the inner one Zero in our calibration, we could get data for the
components that shifted to higher frequency. The frequency shift due to the field for a
peak that moves from xB=0 to xB=B is:
f(xB=B) – f(xB=0). The individual component
frequency shifts, in left to right order, are +9, -9, +9 and -8 GHz. Our line shape model
predicts the apparent peak to peak splitting between the components shifted outward and
inward as 2.04 B B in energy units (or 2.04 h-1B B in frequency units).
Exercise: The average peak to peak separation in the example above is 17.5 GHz which
we model as 2.04 h-1B B. A field measurement yields 6200 Gauss. What is the field
strength in Tesla? Compute B using the date provided. Compare the answer with the
accepted value for the Bohr magneton. Note that the result is unchanged if we add 75
GHz to each frequency as directed by the previous footnote.
Resolving the individual components of the green transitions requires resolving lines
separated by ½h-1BB or about 7 GHz for a field of 1 Tesla. The apparatus used in the
experiment may not be capable of this so it will be difficult to verify the details of the
nine component pattern.
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
Condition to resolve two lines. On can barely resolve two lines if there are separated by
the full width at half maximum of the individual lines. At that separation, a small dip
(about 8%) can be observed in the total intensity curve.9
No dip not resolved.
Plot[{ Exp[-.693 (x - 2)^2/1], Exp[-.693 (x - 4)^2/1],
Exp[-.693 (x - 2)^2/1] + Exp[-.693 (x - 4)^2/1], 1/2}, {x, 0, 6}]
FWHM
FWHM
Resolving the two lines becomes more complicated if one is more intense than the other.
For a 2:1 ratio and lines separated by their (FWHM) one observes
In the case of the lines for the mercury green, the outer two outer two lines are in the
ratio of 3:1 and the separation is the FWHM of each line.
9
Students have access to Mathematica and other programs under MyUTSA/MyUTSA Apps. You can make the plots.
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
Each line grouping has three components spaced by ½BB with intensity ratios 6:3:1.
We see that the peak position is only slightly shifted from the position of the most intense
component, and we note that the least intense outside component could easily get lost.
Review the color adjustment procedure.
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
Line Width Estimates for the lines: Attempt to observe an increase in the line (ring)
widths of the line rings (polarizer horizontal) as you increase the magnetic field
strength? What other change should be observed if the rings increase in width?
Take a zero field image with the polarizer set to pass only the horizontal polarization.
Measure the full width at half maximum (FWHM) of several rings in pixels. Use your
calibration to convert the pixels to frequency. Deduce a best estimate for FWHM of a
single line. At zero field each ring has the same width as that of a single line. One must
consider the color adjustment procedure as one determines the FWHM of a green line.
All the red and blue can be removed. What are the allowed adjustments to the green if the
FWHM is to be measured?
The lines are predicted to have intensities in the ratios of 6:8:6. Using these ratios and a
Gaussian line shape, one predicts that the FWHM of the summed intensity for the three
components with component line center to line center spacing equal to the FWHM of a
single line should be about 47% greater than the FWHM of a single component. (Recall:
Pieter Zeeman received the Noble Prize for observing that spectral lines were
‘broadened’ by a magnetic field. He did not resolve any components or component
groups.)
A Mathematica model follows: See MyUTSA/MyUTSA Apps
(* w2 is the square of the FWHM
d is the component center to component center separation
Adjust mm to be the peak value of the summed line shapes
The intersections with the horizontal line (-4) are ratioed to
provide the overall and that ratio is aplied to the FWHM of a single component
For w2 =1 and d = 1, FWHMnet =((5.47 - 4)/(5 - 4)) * FWHMsingle *)
mm = 14.0; w2 = 1; d = 1; Plot[{6 Exp[-.693 (x - (4 - d))^2/w2],
8 Exp[-.693 (x - 4)^2/w2], 6 Exp[-.693 (x - (4 + d))^2/w2],
6 Exp[-.693 (x - (4 - d))^2/w2] + 8 Exp[-.693 (x - 4)^2/w2] +
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
6 Exp[-.693 (x - (4 + d))^2/w2], mm Exp[-.693 (x - 4)^2/w2],
mm/2}, {x, 0, 8}]
Plot[{6 Exp[-.693 (x - (4 - d))^2/w2], 8 Exp[-.693 (x - 4)^2/w2],
6 Exp[-.693 (x - (4 + d))^2/w2],
6 Exp[-.693 (x - (4 - d))^2/w2] + 8 Exp[-.693 (x - 4)^2/w2] +
6 Exp[-.693 (x - (4 + d))^2/w2], mm Exp[-.693 (x - 4)^2/w2],
mm/2}, {x, 4., 6.0},
GridLines -> {{5.0, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9,
6.0}, {0, 2, 4, 6, 8, 10, 12, 14}}]
Question: In what sense does the overall green line pattern as observed look like the
pattern of the Normal Zeeman Effect?
Question: Do line observations suggest that the patterns are not those of the
Normal Zeeman Effect?
STOP HERE. The study of the Hg yellow lines is a separate experiment. Limit
yourself to green for your first Zeeman experiment.
Part II: The Yellow lines.
The 577/579 nm Lines Data: Our apparatus was designed to analyze the mercury green
line, but the FP etalon does have adequate finesse to provide information about the
mercury yellow lines. This addition information is important because quantum mechanics
makes different predictions for the splitting of the lines due to a magnetic field. Our
analysis will be complicated because our yellow filter passes a ten nm band that includes
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
both yellow lines. An additional problem arises. The yellow lines are not very intense.
We will need to increase the exposure time for each captured image and to add several
images to represent the sum of the individual exposure times.
We will review the predictions for the yellow lines. You are to take data for the lines and
then to try to assign the various ring to either 577 or 579. Finally, compare the patterns
with the predictions.
You must recalibrate for the yellow lines. You should calibrate for each wavelength
separately, but we will use the same calibration for 577 and 579 nm lines.
The yellow line pattern actually has components of two different (zero field) mercury
lines, 577 nm and 579 nm with the 579 line being a little more intense than the 577 line.
The yellow bandpass filter is designed to pass roughly the 578-5 nm to 578+5 nm portion
of the spectrum when the filter is oriented perpendicular to the direction of propagation
of the light. If the filter is rotated away from this normal orientation, the transmitted
spectral range shifts to shorter wavelengths. With care, one can find an angle that
essentially blocks the 579 pattern while passing the 577 thus permitting the overall
pattern to be decomposed into 577 and 579 patterns.
The yellow lines are less intense than the green lines so the exposure time must by
increased to permit analysis of the data. The camera yields 256 grey levels in each color
channel so the intensity for each step is the saturation value divided by 256 (28). If the
intensity were only 10% of the of the saturation value, then the image would have only
26 levels. If the exposure time were increased by a factor of eight, the image would be
displayed as having bright pixels up to the 208th grey level. There is a penalty in that stray
light adds a background to that of the light that holds the data on interest. Try to shield
out stray light.
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
The yellow lines are very weak, so we will slow the shutter speed to a ½ second exposure
and take a set of images for the zero-field pattern. The images are then to be added. Add
the first two using Image Calculator under the Process Menu. Then add each additional
image to the sum of the previous images. Make a profile plot after adding 4 (or 8)
images. Predict the total number of images that need to be added to reach a maximum
grey level of about 200. Make a plot profile when you reach this number. If it looks good
proceed to the analysis. In the case of an applied field, you will probably need 16 to 64
individual images. Beware! You must not exceed a brightness level of 255. Some image
processing procedures execute modular arithmetic. That is: For an 8 bit camera (0 to
255), summing brightness levels of 130 and 130 one gets 260 or 255 + 5 which is
represented as 004. (Note 255 + 1 000; 255 + 2 001; … )
Mercury 579 nm Zeeman Pattern
3
D1
|1 1ñ
ED + 1/2 BB
|1 0ñ
ED
|1 -1ñ
ED - 1/2 BB
|1 1ñ
1
P1
EP + BB
g=1
|1 0ñ
|1 -1ñ
g =1 /2 ;
mJ = - 1,0,1
EP
EP - BB
mJ = - 1, 0, 1
The level diagram for the 579 nm transition in a magnetic field.
Quantum Mechanics Predicts:
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
Upper: 3D1 gu = ½
Mercury Yellow: 579 nm
g 1
J ( J 1) L( L 1) S ( S 1)
2 J ( J 1)
Lower: 1P1 g = 1
; E = Eo + g mJ
As viewed along a direction perpendicular to the field, the components polarized parallel
to the field are labeled as lines and correspond to transitions for which mj = 0. The
components polarized perpendicular to the field as labeled as lines and correspond to
transitions for which mj = .
The 579 pattern is less and less intense as the filter is rotated from normal to the light
path. Propose a procedure to reveal the intensity pattern of the 579 lines. Discuss your
results. List and discuss the aspects in which the pattern differs from the pattern as
predicted by classical physics.
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
Mercury 577 nm Zeeman Pattern
|2 2ñ
ED + 7/3 BB
|2 1ñ
ED + 7/6 BB
3
D2
|2 0ñ
ED
|2 -1ñ
1
P1
ED - 7/6 BB
|2 -2ñ
ED - 7/3 BB
|1 1ñ
EP + BB
EP
EP - BB
|1 0ñ
|1 -1ñ
7
g = /6 ;
mJ = - 2, …. , 2
g=1
mJ = - 1, 0, 1
Complete Quantum Mechanics Predictions:
Mercury Yellow: 577 nm
Upper: ____ , Su = ___ , Lu = ___ , Ju = ___, gu = ___
Lower: _______ S = ___ , L = ___ , J = ___, g = ____
g 1
J ( J 1) L( L 1) S ( S 1)
2 J ( J 1)
; E = Eo + g mJ
As viewed along a direction perpendicular to the field, the components polarized parallel
to the field are labeled as lines and correspond to transitions for which mj = 0. The
components polarized perpendicular to the field as labeled as lines and correspond to
transitions for which mj = .
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
Mercury 577 nm Zeeman Structure
No intensity information.
vo + h-1BB
vo - h-1BB
Lines
m = 0
vo
h-1BB
h-1BB
In each set of three lines
The line to line spacing is:
1
/3 h-1BB
Lines
m = 1,-1
No relative intensity information is available at this point. Assume that the + to maximum spacing is 7/3 BBh-1. Analyze the images to find B. Comment on any
observation that supports the pattern as predicted above. As you analyze your ring
patterns, identify the cases in which it may be difficult to separate all the components
from one another. We should hope to separate the + from the - components in all cases.
(Recall: Pieter Zeeman received the Noble Prize for observing that spectral lines were
‘broadened’ by a magnetic field. He did not resolve any components or component
groups.) Orient the polarizer to pass only the lines. Comment on the manner in which
the net line intensity should increase as the field strength is raised to about 1.1 T.
Question: Assume that the lines for the 577 nm are unresolved (appear as a single
line). What peak to peak separation would you expect between the + and - groupings?
What range of separations might be observed for all possible variations of the relative
intensities of the components? NOTE: one expects the line intensities to be symmetric
about vo. That is the intensity for a line vo + is the same as that for vo - .
The 436 nm Violet Line Data:
NOT OBSERVED as the FP etalon coatings are not designed for that wavelength.
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Zeeman Experiment: General Procedures and Cautions
Remove the filter. Now all the visible lines of mercury are contributing, but the 436 nm
line dominates.
Mercury Violet 436 nm
g 1
Upper: 3P1
gu = 3/2
J ( J 1) L( L 1) S ( S 1)
2 J ( J 1)
Lower: 3S1 g = 2
; E = Eo + g mJ
Mercury 436 nm Zeeman Pattern
|1 1ñ
3
P1
EP + 3/2 BB
|1 0ñ
EP
|1 -1ñ
EP - 3/2 BB
|1 1ñ
3
S1
ES + 2BB
g=2
|1 0ñ
|1 -1ñ
g =3 /2 ;
mJ = - 1,0,1
ES
mJ = - 1, 0, 1
ES - 2BB
Zeeman Procedures and Cautions
} +
}
}
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Zeeman Experiment: General Procedures and Cautions
Again, the components are not resolved. The components split out from zero (some
multiple of 75 GHz.) the interval between the positively shifted ring peak and the
negatively shifted ring peak modeled to be about 3.1 BB.
2.0
1.5
1.0
0.5
4
2
2
4
Intensity vs. energy in units of ½ BB.
For w = 0.8, the to ring separation is modeled to be 3.1 in units of BB. Repeat the
procedures used in the case of the green line.
Reports must address the following as well as report on the experiment in general:
Did you observe the predicted line structures qualitatively? Determine the value of the
Bohr magneton B with uncertainties from you measurements assuming that the proposed
line components models are valid.
Mercury Deep Violet 405 nm Line:
Upper: 3P0
gu = *
Lower: 3S1 g = 2
NOT OBSERVED as the FP etalon coatings are optimized for 546 nm and
wavelengths a little longer plus the intensity at 405 nm is small.
g 1
J ( J 1) L( L 1) S ( S 1)
2 J ( J 1)
;
E = Eo + g mJ
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
* the g factor for a J = 0 state can be set to 3/2 or any other finite value as in this case mJ
has only one value, 0.
Mercury 405 nm Zeeman Pattern
3
P0
|1 0ñ
EP
|1 1ñ
3
S1
ES + 2BB
g=2
|1 0ñ
|1 -1ñ
g =3 /2 ;
mJ = 0
ES
mJ = - 1, 0, 1
ES - 2BB
+
The 405 nm line is lost in the glare of the much more intense 436 nm line. We may be
able to observe component to component separation for this line if we can get a filter that
will block all the other visible lines. (In the case of the intense 436 nm line, all the other
lines contribute only as a little noise in the 436 pattern.) The 2 BB spacing might suggest
that the 405 nm pattern can be resolved. Unfortunately, the resolving power of the etalon
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
fades rapidly for radiation deeper into the violet. If we get a filter, we might see of the spacing can be resolved or at least the - spacing.
Zeeman Line Patterns for Various Transitions of Neon
www.ifm.liu.se/courses/tffm08/dloadsExfys/Lab24Zeeman.pdf
The video capture method discussed immediately below is only to be used if the
Dazzle DVC100 USB capture device fails.
Zeeman Procedures and Cautions
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Zeeman Experiment: General Procedures and Cautions
The old video capture card and software:
The yellow RCA plug of the video out cable should be in the rightmost (AV1) jack of
the video capture board as viewed from the back. Start the ZEEMAN program*:
MENU Video Card Connect (Be sure that the video cable is plugged into the camera.)
MENU Action Video Setup Format: NTSC. Reset format as NTSC.
Once, the NTSC format is set, the image should be clearly displayed on the computer monitor.
Capturing image files: MENU Action Capture Save: JPEG
* Click carefully to start only one copy of the Zeeman program. Launching two or more
copies leads to disaster.
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Zeeman Experiment: General Procedures and Cautions
Zeeman Procedures and Cautions
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