Zeeman Manual

8/6/2019 Zeeman Manual

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Zeeman Effect Laboratory Manual

McGill University

2007

Contents

1 Introduction 1

2 Experiment 1

2.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Appendix A The Lummer-Gehrcke Plate Interferometer 4

Appendix B Additional notes on Zeeman effect 8

B.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9B.2 Zeeman Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Appendix C Refractive Indices 11

1 Introduction

The object of this experiment is to investigate the interaction of atomic angular momentum states, i.e.

atomic magnetic moments, with a magnetic field (The Zeeman Interaction). This magnetic interaction is

one of the weakest studied by physicists. The sophisticated optical equipment available enables the precise

measurement of energy changes as small as 105 eV. This degree of sensitivity is obtained using an optical

interferometer. Normal spectrometer resolving power (/ where , can be resolved at ) is greatly

enhanced by employing the principle of division of amplitude by multiple reflections in the interferometer.

The multiple beams produced are mutually out of phase by the same amount and interfere in the image plane

of the spectrometer to produce a simple interference pattern which obeys the usual criterion for constructive

interference, that nx = d() where d is the path difference between any two successive beams. This pattern

is very sensitive to changes in wavelength so that small wavelength (energy) changes may be determined

from measurements made on the interference pattern, which may itself be recorded using a CCD camera.

Recommended: Tolansky, High Resolution Spectroscopy

2 Experiment

In this experiment, you will use a Lummer-Gehrcke interferometer in combination with a constant deviation

prism. The setup is shown in figure 1.

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0 0 0 0

0 0 0 0

0 0 0 0

1 1 1 1

1 1 1 1

1 1 1 1

0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1

2

4

7

8

9

10

11

12

1

563

Figure 1: Experimental setup for the Zeeman experiment. The spectral tube (1) is placed in the center of the electromagnet (2).The light goes through a lens (3) that focuses the beam on the slit at the entrance of the collimator (4). Optionally it is passesin a polarizing filter (5). It then enters the L-G plate (6), then it is deviated by the constant deviation prism (7), which can berotated with the milled ring (8). Then it is either observed through the telescope or sent to the camera (9), whose telemetricphoto objective (zoom) is set to maximum and focused to infinity. The computer (10) analyzes the resulting pictures. Themagnetic fields intensity is adjusted by its power generator (11), the voltage sent being monitored by a voltmeter (12).

The neon discharge tube is placed at the center of a region of constant high magnetic field. This field

is generated by an electromagnet powered by a large power supply from which we monitor the voltage

with the help of a voltmeter. Light emitted in these conditions from the tube enters the spectrometer. It

passes through a slit into the collimator (a series of lenses). The light is then constrained to go through

a polarization filter (optional) and a Lummer-Gehrcke plate interferometer (described in greater detail inappendix A). It then goes through a constant deviation prism which separates the different wavelengths

horizontally.

2.1 Procedure

Focus the spectrometer telescope at infinity (parallel light rays and observe the neon spectrum through

the spectrometer locating the line corresponding to = 626.6 nm (dark orange) or another line showing

the normal Zeeman effect (see Appendix B).

Move the spectrometer across the field of illumination to obtain maximum intensity. Align source,

collimator axis and focusing lens carefully. Place the Lummer-Gehrcke (LG) interferometer on the spectrometer table. LG requires no adjustment

prior to use.

Observe the interference pattern.

Decrease the slit width until only a broken line or series of dots is seen.

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Observe that each position of constructive interference (dot) is split into 3 by the application of a

magnetic field (Normal Zeeman Effect). Include the polarizing plate so that only polarized light enters

the spectrometer and observe that the three dots correspond to light linearly polarized in orthogonal

directions. Replace the telescope with the CCD camera, which you must focus at infinity. Acquire a

trial image with the camera to determine a suitable exposure time. Acquire images at different fields

and analyze results according to Tolansky, High Resolution Spectroscopy.

2.2 Discussion

The Zeeman Effect and the difference between the Normal and Anomalous Zeeman effect.

The angular momentum of the initial and final atomic states necessary to give a Normal Zeeman

pattern and deduce possible transitions.

Deduce the dependence of the energy of a magnetic moment upon the applied magnetic field and hence

the value of the Bohr magneton.

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Appendices

A The Lummer-Gehrcke Plate Interferometer

Object: To use the Lummer-Gehrcke Plate to observe the Zeeman Effect in the Neon Spectrum, and to

determine e/m for the electrons.

References:

Woods Physical Optics, p.317

Worsnop and Flint, p.345

F. Simeon, Jour. Scientific Instruments, Vol. 1, p.296, 1924

W. E. Williams, Applications of Interferometry, p.94

Apparatus: Lummer-Gehrcke Plate; auxiliary spectrograph; fixed magnet and means to measure the

magnetic field between its poles; neon discharge tube.

Theory: The Lummer-Gehrcke Plate is a glass plate, whose surfaces are accurately plane and parallel

to each other. Monochromatic parallel light is introduced into the plate at almost grazing incidence, and

undergoes successive internal reflections at the surfaces of the plate. At each reflection, some of the light

emerges from the plate. Under appropriate conditions, the light at each reflection is in phase with the light

which emerged at the previous reflection. All these emergent rays of parallel light reinforce, and may be

brought to a focus by a lens. (The light is usually introduced by means of a prism cemented to the plate, to

avoid loss of intensity by reflection at the surface of the plate).

A

C

D

B

t90

Figure 2: Lummer-Gehrcke plate interferometer

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Let t be the thickness of the plate and its refractive index, then, the retardation between the two

consecutive rays will be:

d = (AB + BC) AD

= 2t(sec ) 2t(tan sin ).

From Snell-Descartes law, we know that sin = sin , which implies:

d = 2t (sec tan sin )

= 2t sec

1 sin2

= 2t cos . (1)

The condition for constructive interference is d = n. Expressing the last relation in terms of :

n22 = 4t22

1 sin2

n = 2t

2 sin2 . (2)

This implies that the order of the spectrum (n) may be found if the wavelength and the index of refraction

are given, with sin 1.

If the light is not only indicent at the same angle , there will also be reinforcement in other directions,

corresponding to orders differing from n. In practice, the Lummer-Gehrcke plate may be placed between

the collimator and the prism of a spectroscope. Each line of a spectrum is nearly monochromatic and is

observed as a series of dots instead of a continuous line. Each of the observed dots correspond to a different

order of the spectrum.

Separation of the orders Let be the variation in the angle of emergence for a change of one in the

order, from the nth to the (n + 1)th. Differentiating the square of (eq. 2), one obtains:

2n2 dn = 8t2 sin cos d,

n2 dn = 2t2 sin2 d,

in terms of variations:

= n2

2t2 sin2n. (3)

We are interested in n = 1 and we want to eliminate n:

=

2 sin2

t sin2(4)

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0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

s m

n + 1n

Figure 3: Main and satellite lines with appropriate distances

To evalutate sm

m2

, you may determine the order of the spectrum from (eq. 2). t, and

are

characteristics of the plate supplied by the manufacturer. You may want to draw a dispersion curve. You

should consult appendix C for details about the refractive indices. The intersting values are listed in column

BK7 of each table; they are valid for a plate thickness t = 0.4853 cm.

Zeeman Effect It may be shown that the wavelength of light is changed by when the emission

source is placed in a magnetic field in the domain of the Normal Zeeman effect we have:

e

m=

4c

H

s2

, (11)

where, e is the charge of the electron, m is its mass, c is the speed of light in vacuum and H is the strenght

of the field. Measurements of and H allow an experimental value of em

to be calculated using the latter

relation.

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B Additional notes on Zeeman effect

References:

H. E. White, Introduction to Atomic Spectra, p. 149

Back and Lande, Zeemaneffekt

If a source of light is placed between the poles of a magnet and its spectrum is observed with a high

resolution instrument, as the field strength is increased, the spectral lines are seen to widen, and finally to

split up into a symmetrical pattern. The first lines for which the effect was carefully studied by Zeeman

in 1896 were found to split into triplets and this behaviour was regarded as Normal. One component

remained in the undisturbed position., with a companion on each side, whose change in frequency was given

by the relation was given by the relation:

=eH

4m(12)

where, e is the electronic charge, H is the magnetic field, and m is the electronic mass.

Actually, many lines exhibit an Anomalous Zeeman Effect instead of this normal separation; the pattern

may consist of several components whose displacements maybe expressed as simple fractious of the normal

serration Runges Law.

Also, it has been found that all of the lines of any spectrum series (lines produced by the emission of

energy as an electron returns from any possible disturbed level to one particular level) have similar Zeeman

patterns Prestons Law. This similarity of behaviour is a powerful tool for the classification of spectra.

If the magnetic field is continuously increased, at first the separations increase proportionally, then the

patterns of lines which behave anomalously change, finally taking the form of the normal triplet - thePaschen-Back Effect. The field magnitude required depends on the nature of the lines. It is now possible

from Quantum theory considerations to predict satisfactorily the Zeeman patterns for various spectra.

If the Zeeman pattern is observed in a direction at right angles to the magnetic field, some of the component

lines are found to be plane polarized in the direction of the field, the others are plane polarized perpendicular

to the field. If the pattern is observed along the field, some components are ford to be circularly polarized,

some are missing altogether.

The pattern is commonly observed across the field, and the components are reported as p or (parallel)

and s or . perpendicular (German senkrecht), according to the polarization, either parallel or perpendicular,

respectively, to the field.

Consider, for example, a line whose Zeeman pattern is reported as on figure 4.

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6(0) (1) (2) 6 7 8 9 10p

s

Figure 4: Example of a Zeeman pattern

This means that the pattern is symmetrical, the Runge denominator is 6, the parallel (p or n) components

are displaced from the undisturbed frequency by 0/6, 1/6, 2/6 of the normal frequency separation, while the

perpendicular (s or ) components are displaced 6/6, 7/6, etc.

The pattern may be indicated diagrammatically as above, where the dots represent the normal sep-

arations and the lengths of the lines represent the intensity of the p and s components. In the present

experiment, the Zeeman Effect will be studied for some lines in the Neon spectrum. The separation of a

Nominal triplet will be measured, and used to determine a value of e/m for the electron. Also, some of the

more complicated patterns will be compared with the accepted observations of Lande.

B.1 Procedure

With a neon discharge tube as Source, line up the spectrograph for visual observation. Open the slit

as wide as possible without causing the lines to overlap.

Place the Lummer-Gehrcke plate in position between the collimator and the prism, and adjust it to

give a clear pattern.

Mount the magnet in front of the spectroscope, with the poles at the height of the slit. Move the

magnet up to the discharge tube, so that the discharge observed comes from the strong magnetic field

between the poles. Observe the Zeeman patterns produced. Move the magnet to give a weaker field,

and note how the patterns close in. Observe the spectrum through a Nicol prism (or Polaroid) andnote the effect of rotating the Nicol.

Replace the observing telescope by the CCD camera, and using the Liner Plate to obtain images of:

1. The Neon spectrum with no magnetic field.

2. The Neon spectrum with maximum magnetic field.

3. The Neon spectrum with maximum magnetic field through the Nicol set to transmit horizontally,

then vertically.

4. The Neon spectrum with low magnetic field.

Measure the field of the magnet with a ballistic galvanometer, or use given value.

Identify the Neon lines from the images obtained from the CCD camera.

Measure the Zeeman separation for the line = 6266A which exhibits the Normal Zeeman Effect, and

calculate a value of e/m for the electron (see page 7). You could alternatively use another spectral line

showing the Normal Zeeman Effect.

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Measure up any other lines that you have time for, and see if your analysis of the components agrees

with that given by Lande.

B.2 Zeeman Patterns

(A) (A)

7032 (0) (1) 2 3 42 6217(0) 4 (5) 9 14

6

6717(1) 30 31

30 6164(0) 4

3

6678(0) (8) 31 39 47

30 61438 (16) 29 37 45 53

30

6599 (69) 31 39 4030 6096(0) (5) 34 39 44

30

6532 (0) 23 6074(0) 22

15

6507 (0) (5) 12 17 2215 6029(2) 20 22

15

6382 10 (12) 2215 5976(0) (1) 2 3 4

2

6334 (0) (1) 2 3 42 5945(2) (4) 11 13 15 17

10

6304 (0) (7) 30 37 4430 5882 (0) (1) 8 9 106

6266(0) 1

1 5852(0) 31

30

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C Refractive Indices

Reference: Optics Guide 3, Melles Griot, pp. 58-60.

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