The Anomalous Zeeman Splitting of the Sodium 3P States

Transcription

1 Advanced Optics Laboratory The Anomalous Zeeman Splitting of the Sodium 3P States David Galey Lindsay Stanceu Prasenjit Bose April 5, 010

2 Objectives Calibrate Fabry-Perot interferometer Determine the Zeeman splitting of the 3P energy state of the Sodium atom Determine effective nuclear charge of sodium atom Determine strength of internal magnetic field

3 Zeeman Effect - Historical Origin Zeeman Effect is named after Dutch Physicist, Pieter Zeeman. The experimental Evidence of this effect was published in: i) P. Zeeman, "The" Effect of Magnetisation on the Nature of Light Emitted by a Substance" Nature 55: 347. (1897) ii) P. Zeeman, "Doubles" and triplets in the spectrum produced by external magnetic forces". Phil. Mag. 44: 55. (1897) He obtained the Nobel Prize for Physics in 190. Dr. Pieter Zeeman

4 Zeeman Effect Zeeman Effect is the splitting of spectral lines into multiple lines in the presence of a static magnetic field Modern Uses: Nuclear magnetic Resonance Spectroscopy Electron-spin resonance spectroscopy Magnetic Resonance Imaging Mössbauer spectroscopy

5 Sodium Doublet A sodium Yellow doublet transition happens because of transition from 3p to 3s transition. The 3p level is split into states with total angular momentum (jl+s l+s) ) of j3/ and j1/ by the magnetic energy of the electron spin in the presence of the internal magnetic field caused by the orbital motion. In the case of the sodium doublet, the difference in energy for the 3p 3/ and 3p 1/ comes from a change of 1 unit in the spin orientation with the orbital part presumed to be the same.

6 Sodium Doublet Continued Energy Difference For Sodium doublet, j 1 as there is only spin shift from 1/ to -1/ or viceversa (m remains same) g Gyromagnetic ratio B magnetic field produced by the Nucleus when observed from the electron reference frame (Classical View point)

7 The Fabry-Perot Interferometer Path Difference for bright fringe: n f d(cos( θ )) mλ Fringes result from interference between multiple reflected beams, with bright fringes corresponding to constructive interference and dark fringes to destructive interference

8 Theory Fringe Patterns from Wavelength Components of light source coincide when: OPL OPL m λ m λ 1 1 Next Coincidence occurs at: ( m λ 1 + n) λ 1 ( m + n + 1) Where n number of fringes between coincidences λ λ λ 1 λ n

9 Theory Number of fringes is can be related to the mirror displacement by: Therefore, the difference in wavelengths is approximately: λ n d λ 1 λ 1 λ d d However, using average wavelength gives a more accurate result: λ avg () λ d (1) Since the average requires both wavelengths to be known, with only 1 wavelength, equation 1 can be used to get a first approximation. The results can then be used with equation to get a more accurate value.

10 For reflectivity of R0.85, Coefficient of Finesse: Theory Question 1/ π ( F) Finesse: F Minimum Wavelength Increment: ( λ ) F λ0 Finesse*n 4R (1 R) 4*0.85 (1 0.85) ( nm) 19.31* *1*159149nm 0 min f d Free Spectral Range: ( min nm λ0 ) FSR Finesse*( λ0) 19.31* nm ( λ 0 ) FSR nm Resolving Power: R λ nm * 10 nm ( λ ) nm 0 min

11 Theory Question Minimum Frequency Increment: ( υ 0 ) min c ( λ ) c ( λ ) min 5.319Hz 8 3*10 m / s *10 m ( υ0) min 0 Free Spectral Frequency Range: 8 3*10 m / 1.089*10 ( υ0) FSR 9 0 FSR s m ( υ 17 0) min.755* 10 Hz

12 Experimental Setup Laser Source Mirrors Diverging lens Telescope Micrometer Mirrors

13 Experimental Setup Telescope Movable mirror Collector lens Stationary mirror Mirror adjustment bar Micrometer

14 Procedure Calibration Assemble Fabry-Perot interferometer with the mirrors close, but not touching Record the value on the micrometer Rotate micrometer and count the number of fringes that pass Record the micrometer reading every 50 fringes until 500 fringes have passed

15 Procedure Calibration

16 Procedure Calibration Convert fringe count to mirror displacement and plot mirror displacement vs. micrometer displacement Slope of graph is the calibration factor, the amount the mirror moves per tic on the micrometer

17 Experimental Setup - Sodium Sodium lamp Filter Precision leveling device (Handbook of Mathematical Functions) Interferometer (same setup as laser)

18 Procedure Sodium Doublet Replace laser source with sodium source Sodium produces sets of fringe patterns Adjust mirror separation until patterns are coincident (each fringe is made up of closely spaced lines) Rotate micrometer in both directions and record position where the close lines start to blur, average the two numbers to determine the position of coincidence Rotate micrometer further and find another position of coincidence Repeat for 6+ coincidences

19 Procedure Sodium Doublet

20 Procedure Sodium Doublet

21 Procedure Sodium Doublet

22 Procedure Sodium Doublet Convert micrometer displacements to mirror displacements using previous calibration factor Plot mirror displacement vs. coincidence number Slope is d, the distance the mirror must move between two coincidences Calculate the energy difference between the two 3p states Using that, calculate the effective nuclear charge and the magnetic field

23 Results - Calibration MirrorDisp lacement FringeCoun t *Wavelength

24 Results - Calibration Calibratio nfactor ( ± E 3) µ m

25 Results Sodium Double (Trial 1) AvgCirc Re ading Circular Re ading1+ Circular Re ading CircDisplacement AvgCirc Re ading MirrorDisp lace CircDispla cement * Calibratio nfactor

26 Results Sodium Doublet (Trial 1) d ( ± 0.65) µm

27 Results Sodium Doublet (Trial 1) λ 1theo λ 1theo : nm λ 1 : d nm λ : λ λ 1 for i λ λ 1theo λ ( ) λ 1theo + λ λ avg λ λ avg d λ λ theo nm λ : λ 1theo λ : 0.597nm λ theo : nm nm ( ) 100 λ λ theo %err λ :.13 λ theo ( ) 100 λ λ theo %err λ : λ theo

28 Results Sodium Doublet (Trial 1) Energy separation between states: E : ( h c λ ) λ avg J Internal magnetic field: E E ev : J %err : ( ) 100 E ev E evtheo E evtheo Effective nuclear charge: n : 3 l : 1 E evtheo : m s : e : C h b : s m e : kg B : E ev h b m s e ( B 18T) 100 %err B : 18T m e T E ev n 3 l ( l + 1) Z eff :

29 Results Sodium Double (Trial ) AvgCirc Re ading Circular Re ading1+ Circular Re ading CircDispla cement AvgCirc Re ading MirrorDisp lace CircDispla cement * Calibratio nfactor

30 Results Sodium Doublet (Trial ) d ( 83.7 ± ) µm

31 Results Sodium Doublet (Trial ) λ 1theo : nm λ 1theo λ 1 : d nm λ : λ λ 1 for i λ λ 1theo λ ( ) λ 1theo + λ λ avg λ λ avg d λ nm λ theo : 0.597nm ( ) 100 λ λ theo %err λ :.507 λ theo λ : λ 1theo λ ( ) nm λ λ theo %err λ : λ theo

32 Results Sodium Doublet (Trial ) Energy separation between states: E : ( h c λ ) λ avg J Internal magnetic field: E E ev : J %err : ( ) 100 E ev E evtheo E evtheo Effective nuclear charge: n : 3 l : 1 E evtheo : m s : e : C h b : s m e : kg B : E ev h b m s e m e ( B 18T) 100 %err B : 18T T E ev n 3 l ( l + 1) Z eff :

33 Conclusions Wavelength separation λ nm ( ) 100 λ λ theo %err λ :.13 λ theo λ nm ( ) 100 λ λ theo %err λ :.507 λ theo Energy difference E : ( h c λ ) λ avg J E : ( h c λ ) λ avg J E E ev : J %err : ( ) 100 E ev E evtheo E evtheo %err : E E ev : J ( ) E ev E evtheo E evtheo

34 Conclusions Effective nuclear charge E ev n 3 l ( l + 1) E ev n 3 l ( l + 1) Z eff : Z eff : Magnetic field B : E ev h b m s e m e T ( B 18T) 100 %err B : 18T B : E ev h b m s e m e ( B 18T) 100 %err B : 18T T 4.659

35 Conclusions/Observations Interferometer is extremely difficult to align and keep aligned, slightest bump throws the whole thing off, had to re-align using laser When rotating micrometer to increase mirror separation, spring pulling mirror back did not always do so smoothly or had to be manually pushed back Fringes became narrower as mirror separation decreased, made it very hard to see if there was coincidence or not Results ended up being very accurate despite problems, because once it was aligned and your eyes were used to seeing the fringes, they were extremely clear and could easily be read

36 Sources of Error Eyestrain Too much staring at fringes in one day and they start to be harder to focus on Random Measurement limitations Micrometer precision was limited Random Minor misalignment Mirrors might not have been perfectly parallel, could throw readings off slightly Random Resolution of device Though we used the range of positions where we could separate the e two closely spaced lines as our coincidence range, we could not resolve the fringes enough to be able to identify the exact position of maximum coincidence Narrow fringes at smaller mirror separation made position of coincidence even harder to see Systematic device limitations Random human vision limitations

37 References Advanced Optics Laboratory manual Lecture notes astr.gsu.edu/hbase/quantum/sodzee.html Beiser,, Arthur. Concepts of Modern Physics, 6 th ed. rference/multiplebeaminterferencenotes.html %3Bjsessionid5FA663719B44787A BE6CE