Instytut Fizyki Doświadczalnej

Instytut Fizyki Doświadczalnej Wydział Matematyki, Fizyki i Informatyki

UNIWERSYTET GDAŃSKI

Instytut Fizyki Doświadczalnej 1.

Experiment 30 : Normal and anomalous Zeeman effect

I. Background theory.

1. Energy levels of electrons in atoms. 2. Quantum numbers of electron energy levels. 3. Magnetic moment of the electron shell of an atom:

a) orbital magnetic moment; b) spin magnetic moment.

4. Atoms in a constant magnetic field: a) Larmor precession; b) Larmor precession frequency; c) Landé factor.

5. Effect of a magnetic field on the wave functions and energy levels of an atom. 6. Normal Zeeman effect:

a) Zeeman singlet splitting; b) Bohr magneton; c) selection rules for ∆𝑀𝐿; d) separation of Zeeman sublevels.

7. Lorentz's theory: a) 𝜋 and 𝜎 components of Zeeman singlet splitting; b) polarisation of 𝜋 and 𝜎 components; c) Lorentz triplet.

8. Anomalous Zeeman effect: a) anomalous Zeeman effect energy level splitting; b) Landé factor.

9. Experimental setup for the study of the transverse and longitudinal Zeeman effect. 10. The construction and use of a Fabry – Pérot interferometer.

11. Definition of polarised light. 12. Using waveplates to change the polarisation of light. 13. Interference filter parameters.

II. Experimental tasks.

1. Familiarise yourself with the experimental setup shown in Picture 1.

2. Prepare the experimental setup to study the Zeeman effect. To do this, follow these steps: ensure that the transformer’s current knob (5, Picture 1) is set to position “0” and then turn on the power to the transformer and cadmium lamp (3, Picture 1) (their switches are on the rear of the housings). Turn on the ammeter (6 in Picture 1).

The digital meter shuts down automatically after a certain period of inactivity. Ensure that the ammeter remains on during measurements, turning it on again if necessary.



Turn on the computer and start the CCD camera preview (follow the instructions in Appendix A).

3. Record the red cadmium line (λ = 643,847 nm) splitting in the normal Zeeman effect. To do this, ensure that the magnetic field is perpendicular to the optical axis (the swivel table with electromagnet can be unlocked using the screw underneath). Place the red filter (7, Picture 1) in the interferometer slit and set the analyser’s orientation (1, Picture 1) to vertical.

4. Gradually increase the current flowing through the coil of the electromagnet (with the knob on the transformer’s front panel 5, Picture 1) until splitting interference fringes are visible.

5. Record images using the CCD camera (following Appendix A) while increasing the current in steps of 1 A.

6. Change the orientation of the analyser’s polarisation to horizontal and record images while changing the magnetic field strength.

7. Using the electromagnet characteristics sheet in Appendix C, measure the magnetic field strength 𝐵 for each value of the current 𝐼.

8. Analyse the results of measuring the Zeeman effect: a) Use Appendix B or the instructions for the CCD camera control software (part 11. in IV.) to

measure the interference rings on the recorded images; b) Plot a graph of the ratio 𝛿/Δ as a function of magnetic field strength 𝐵;

Picture 1. Experimental setup for studying the Zeeman effect: 1 – optical bench including (from left to right): CCD camera (in mounting), lens +50 mm, analyser, waveplate bracket, green filter bracket, lens +300 mm, Fabry – Pérot interferometer (with red filter holder), lens +50 mm; 2 – swivel table with electromagnet and cadmium lamp; 3 – lamp power supply; 4 – capacitor; 5 – transformer; 6 – digital multimeter (ammeter); 7 – accessories (from left to right):green filter in bracket, red filter, quarter waveplate in bracket; 8 – computer.

Do not exceed a current of 9 A through the electromagnet coils. To prevent overheating, turn the transformer’s current knob to minimum after completing the tasks.



c) Calculate the Bohr magneton 𝜇𝐵 and electron specific charge 𝑞� = 𝑒/𝑚𝑒 (including uncertainties);

d) Compare your results with the data given in the literature.

9. Explain the interference images in II.6. 10. Record the cadmium spectral line splitting (λ = 508,588 nm) for the anomalous Zeeman effect.

Ensure that the magnetic field is perpendicular to the optical axis. Remove the red filter from the Fabry – Pérot interferometer. Insert the green filter (7, Picture 1) in its mounting (1, Picture 1) (possible reflections in the preview from the CCD camera can be eliminated by gently rotating the filter in the horizontal plane). To make measurements of the 𝜎 component of the emitted light, orient the analyser (1, Picture 1) vertically.

11. Increase the current through the electromagnet until splitting interference fringes are visible. 12. Record CCD camera images depending on the electromagnet current. Increase the current in

steps of 0,5 A. 13. Re-orient the analyser in the horizontal direction and repeat measurements for the 𝜋

component. 14. Read off the magnetic field strength 𝐵 for each value of the current 𝐼 in step II.12. in Appendix

C. 15. Analyse your results of measuring the anomalous Zeeman effect:

a) measure the interference rings in your images of the anomalous Zeeman effect; b) Plot a graph of the ratio 𝛿/Δ as a function of magnetic field strength 𝐵 for the 𝜋 and 𝜎

components of the lamp’s spectral lines; c) Calculate the Bohr magneton 𝜇𝐵 and electron specific charge 𝑞� = 𝑒/𝑚𝑒 separately for both

components of emitted light; d) calculate the average value of Bohr magneton and the specific charge of the electron and

compare them with the data found in the literature. 16. Record interference fringes of the normal and anomalous longitudinal Zeeman effect.

To do this, change the orientation of the electromagnet by turning the table so that the direction of the magnetic field is parallel to the direction of the light from the lamp.

17. Select an appropriate filter for the type of Zeeman effect you would like to study. 18. Place a quarter-wave plate in the holder (1, Picture 1). 19. Set a coil current to give a sharp interference pattern on the screen. 20. Record interference images for both Zeeman effects for two analyser orientations i.e., +45° and

-45° relative to the vertical axis. 21. Develop a conclusion from the results of your analysis.

III. Apparatus.

1. CCD camera. 2. 2 lenses +50 mm. 3. 1 lens +300 mm. 4. Analyser. 5. Fabry – Pérot interferometer (etalon size 3∙10-3 m).



6. Green filter (λ = 508 nm) in housing. 7. Red filter (λ = 595 nm) in housing. 8. Quarter-wave plate. 9. Cadmium lamp. 10. Electromagnet. 11. Cadmium lamp power supply. 12. Transformer. 13. Swivel table. 14. Capacitor with capacitance of 22 mF. 15. Universal multimeter. 16. Computer with Motic Image Plus 2.0 ML software program.

IV. Literature.

1. PHYWE “Laboratory Experiment Physics”, 5.1.10-05 Zeeman Effect, www.phywe.com. 2. E.U. Condon & G.H. Shortley – “The Theory of Atomic Spectra”, Athenaeum Press Limited,

Newcastle upon Tyne 1991. 3. H.A. Enge, M.R. Wehr, J.A. Richards – “Introduction to Atomic Physics”, Addison-Wesley,

Reading-Mass, 1981.

4. W.A. Shurcliff, S.S. Ballard – “Polarized Light”, Princeton, N.Y. 1964. 5. V. Acosta, C.L. Cowan, B.J. Graham – “Essentials of Modern Physics”, Harper & Row, N.Y. 1973. 6. H. Haken, H.Ch. Wolf – “The Physics of Atoms and Quanta”, Springer, 2000. 7. R.P. Feynman, R. Leighton, M. Sands – “The Feynman Lectures on Physics”, Vol. II, Part 2 &

Vol.III., Addison - Wesley, 2005.



Appendix A Recording an image using the CCD camera and the Motic Images Plus 2.0 ML software

package

A. Turning on and adjusting the CCD camera preview.

1. Star the program Motic Images Plus 2.0 ML by clicking on the desktop icon (or the start menu).

2. The program main window will open:

3. Click the camera icon located on the upper toolbar (see Picture 2).

The Motic Live Imaging Module will open with a camera preview (Picture 3).

Picture 2. Motic Images Plus 2.0 ML main window: 1 – preview of the currently edited image, 2 – toolbar, 3 – thumbnail list of captured images. Currently selected image is outlined in red.



4. Use the bookmark panel icons (1, Picture 3) to view the different configuration options, making

changes if needed (2, Picture 3), including brightness, colour saturation, contrast, sharpness, etc.

B. Recording images from the CCD camera.

1. Click the camera icon in the Motic Live Imaging Module bookmarks panel (1, Picture 3).

2. Select the output image resolution from the Format drop-down list. It is advisable to store images in the greatest possible resolution for easier processing.

3. Click Capture to capture an image from the CCD camera.

4. A thumbnail will appear in the Motic Images Plus 2.0 ML thumbnail panel (3, Picture 2). By clicking on the desired thumbnail you can view a full preview of the captured image (1, Picture 2).

Picture 3. Motic Live Imaging Module window: 1 – bookmarks panel; 2 – configuration panel; 3 – camera preview panel.

Customizing the CCD camera preview options can improve image clarity. A particularly useful option is digital noise reduction (Remove Noise).



5. Captured images are stored in the folder Capture Folder which has a shortcut on the desktop and start menu. The program saves images in its own SFC format by default. To process them in another program, save them as JPEG or TIFF. To do this:

a) click the thumbnail in Motic Images Plus 2.0 ML; b) when it appears in the preview panel (1, Picture 2), click File and choose Save As…; c) in the next window, enter the name of the selected image, select the file format, specify

the folder where the image is to be saved and click OK.



Appendix B

Making distance measurements from CCD camera images using the program NI Vision Assistant 2009 (for example, interference fringes)

A. General information.

The software program National Instruments Vision Assistant offers the ability to take measurements of geometrical properties of objects shown in raster images, such as distances between points, areas, diameters, etc. The program supports most of today’s popular formats (including *.bmp, *.jpg, *.tif, *.png).

A List of operations performed sequentially by NI Vision Assistant, such as image transformations, distance measurements and conversions is written in a script that appears in the script editing panel (4, Picture 4).

Each step in the current script may be deleted by clicking on the icon, or edited by clicking on or double-clicking on the icon representing a step.

B. Opening and preparing their images for editing.

1. Open a picture (pictures) in NI Vision Assistant in one of two ways:

Picture 4. NI Vision Assistant program window: 1 – function selection panel; 2 – image selection panel; 3 – image preview panel; 4 – script editing panel.



a) click the button on the toolbar of the main window (or select Open Image… in the File menu), and then select the image (images) and click Open;

b) go to the image viewer, click Browse Images on the right of the toolbar in the main window,

click at the bottom of the screen, select the images and click Open.

2. After opening the desired image (images), you can start editing them and making measurements. All operations are found on the image processing tab, accessible by clicking Process Image, located on the right of the toolbar in the main window.

3. At any time, you can select which image to edit with the Process Image tab by clicking in the image selection panel (2, Figure 4), or by going to the browser (click Browse Images) and double-clicking the selected thumbnail image (or selecting the thumbnail with a single mouse-click and going to the Process Image tab).

4. To add new images to the browser, click at the bottom of the screen, then select the image (images) and click Open. Depending on the preferences, a dialogue box will appear asking whether you would like to replace the existing images with the newly selected images.

5. Clicking in the image viewer allows you to switch between a grid view of thumbnails or a single image.

C. Measuring distances between two points.

The program NI Vision Assistant allows you to measure distances between points on images, transforming the distance in pixels into a distance expressed in physical units. To do this, you have to calibrate the image.

Image calibration.

1. Select Image Calibration from the Image menu. The calibration wizard window will appear.

2. Ensure that the first option is selected - Simple Calibration. Click OK.

3. In step 1 (Step 1 of 3) you will see a preview of the currently open image. Ensure that you select square pixels (Square), and click Next.

If after opening, the image (images) appear completely black, you must convert the file by changing its bit-depth. To do this: 1. select the appropriate image and go to the edit tab (Process Image); 2. under the Greyscale menu, select Conversion, and in the function selection

panel (1, Figure 4), choose 8-bit [0, 255] and confirm by clicking OK.

The converted image can be saved by clicking Save Image from the File menu.



4. In step 2 (Step 2 of 3), select two points on the image separated by a known actual distance (e.g., two points on the centimetre scale on the image screen), clicking on the appropriate points in the preview.

In the numeric field in the section Correspondence Image – Real World, enter the physical distance between the selected points and select the appropriate unit (see Picture 5).

Picture 5. Calibration wizard for the program NI Vision Assistant (image preview with two points separated by a known

physical length (1 cm))

5. After setting the reference distance, click Next and then OK. The calibration wizard will close.

6. Confirm the image calibration data by clicking OK in the function selection panel (1, Picture 4).

Measuring distances on images

1. After image calibration, you can make distance measurements between any two points. To do this, click Measure in the function selection panel (1, Picture 4):

2. Select Length from the list of possible measurements in the function panel (titled Measure

Setup).

3. Use the mouse to select the two end points of the segment for the distance you wish to measure. The length of the segment in physical units will be displayed in the table of measurements in the script editing window (Length = …).



4. A series of distance measurements can be made by drawing new segments. Each new measurement will be stored on a separate line in the table.

5. Collected data can be saved as a text file or put in a spreadsheet in Microsoft Excel. To do this, click one of the buttons on the right-hand side of the script editing panel (Save Results or Send Data To Excel). The resulting file can then be imported into any program used for processing and visualising numeric data (e.g.: Origin, Sigma Plot amongst others).

6. To exit the Measure tool, click OK in the Measure Setup panel. You can always go back to the results of your measurements (or take more), by double-clicking the Measure icon in the script editing window.



Appendix C Dependence of magnetic field strength 𝐵 on current 𝐼 through the electromagnet coils in the

experiment for studying the Zeeman effect (for a pole separation distance of 9 mm) Source: Opis układu pomiarowego nr P251105, PHYWE Systeme GmbH & Co. [11]

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