Department of Physics, Middlebury College 1992-93
Modern Physics Laboratory


XX. Independent Project in Experimental
Modern Physics


Discussion

During the two-week period allocated to Expt. XX you will pursue a modern physics experiment of your own choosing. You are free to develop your own idea for a project or work on one of the suggested projects below. Before you get too creative or too ambitious you should be aware of the following constraints.

(1) Only two weeks are available to complete the experimental work for your project and therefore you should not expect to design or construct new apparatus. Plan on using existing equipment in our laboratories.
(2) It is likely that you will have to share equipment with other students and faculty. Be prepared to schedule your work around the time constraints of others.
(3) Some ideas seem incredibly simple on the blackboard but turn out to be impractical or impossible in the laboratory. Discuss your project with the laboratory instructor as soon as possible to be sure that you have an excellent chance for success within the two-week period.

The experiments below have all been performed successfully in our laboratories at some time in the past few years. Some of these experiments are old classics which use specially designed apparatus and involve essentially no risk of failure. Others are closer to current physics research and should only be attempted by those willing to make considerable independent effort. References are given for all experiments and it is suggested that you consult them before deciding on a particular project.

Suggested Projects

(1) Franck-Hertz Experiment

In this classic experiment, a beam of low energy electrons is directed through a low pressure mercury vapor and the transmission of the beam through that vapor is measured as a DC electrical current.1,2,3,4 When an electron collides with a Hg atom in the vapor it can (a) scatter elastically, that is, without loss of kinetic energy, or (b) scatter inelastically, losing kinetic energy to excitation of a Hg atom from the ground state to the first excited state. If the electron current passing through the vapor is measured as a function of electron acceleration energy, one obtains an oscillatory transmission curve, as in Fig. 1. The spacing between the transmission current minima is found to be 4.9 eV, corresponding to the spectroscopically determined energy difference between the 3P2,1,0 first excited states of Hg and the 1S0 ground state, as shown in Fig. 1 of Expt. XIV on the Zeeman effect in Hg. The minima are due to excitation of many Hg atoms by a single electron as it passes through the vapor. When the inelastic excitation probability to the 3P2,1,0 states is high, as it is at the minima of Fig. 1., one observes a sharp increase in the emission of 2536.5 Å "resonance radiation" from the 3P1S1 --> 1S0 transition. Thus, the Franck-Hertz experiment provides important non-optical evidence for the existence of discrete energy levels in atomic systems.

Required equipment includes:
(a) Klinger Model KA6040/KA6041 Franck-Hertz apparatus,
(b) miscellaneous power supplies,
(c) electrometer,
(d) IBM PC computer for controlling acceleration voltage and measuring electrometer current,
(e) possibly the SPEX 1704 spectrometer and associated equipment for observation of resonance radiation.

(2) Millikan Oil Drop Experiment

This classic experiment demonstrates quantization of electric charge and provides a value for the electronic charge e.5,6,7,8 One observes the movement of tiny, charged oil droplets falling through the region between parallel plates held at fixed potential difference. The viscous drag force exerted by the surrounding air on the droplet is appreciable, and when properly accounted for, provides a measure of the radius of the oil droplets. By measuring the velocities for rising and falling electrons at a given potential difference between the parallel plates, one can determine the electric charge on an individual droplet. Droplet charges are observed to be integer multiples of a fundamental unit of electric charge, e = 1.6 x 10-19 C. This experiment should not be attempted by anyone with poor eyesight.

Required equipment includes:
(a) PASCO Model 3000A Millikan oil drop apparatus,
(b) electronic timers,
(c) holy oil, blessed by the Pope,
(d) Cray II for data reduction.

(3) Alpha and Beta Ray Spectroscopy

In Expts. VI through IX of this laboratory manual, the Quantum 8 multichannel analyzer was used with a NaI(T) detector to obtain gamma ray spectra of radioactive sources. The Quantum 8 may also be used to obtain alpha and beta particle spectra when used with The Nucleus Model 5300 Alpha Spectrometer.9 The Model 5300 contains an evacuable chamber in which scattering of alpha and beta particles by air can be eliminated. Alpha and beta particles are detected in a silicon surface barrier detector that is connected directly to the Quantum 8 for pulse height analysis. An alpha particle spectrum taken with a windowless 228Th radioactive source is shown in Fig. 2.10 In Fig. 2 one not only sees a pair of alpha peaks from the 228Th parent, but also peaks due to alpha decay of the 224Ra, 220Rn, 216Po, and 212Bi, alpha-unstable daughter nuclei in the thorium decay series.11 The energies of the alpha particles can be used to establish nuclear mass differences and nuclear excited state energies. Beta particle spectra can also be obtained with the Model 5300 Alpha Spectrometer.

Required equipment includes:
(a) The Nucleus Model 5300 Alpha Spectrometer,
(b) vacuum roughing pump and vacuum gauge,
(c) windowless radioactive sources.

(4) Scintillation Spectrum of T Impurities in NaI(T)

The primary energy loss mechanisms for low energy gamma rays in a NaI crystal are (a) Compton scattering, and (b) the photoelectric effect. In both processes, energetic electrons result and these electrons rapidly lose their kinetic energy by exciting other electrons in the crystal lattice. Following this excitation, a crystal lattice such as NaI comes to equilibrium predominantly through non-radiative processes, such as phonon emission. However, if a number of T atoms are added to the lattice, the excited lattice energy can be transferred to T "activator" atoms which fluoresce in a broad peak near 4100 Å.12,13 This light can then be transferred to a photomultiplier tube where an electrical pulse is generated. It is important to determine the T fluorescence spectrum so that a photomultiplier tube of appropriate wavelength sensitivity is used with the scintillator.

Required equipment includes:
(a) SPEX 1704 Spectrometer, data acquisition electronics, and IBM PC/XT computer,
(b) electronic chopper for chopping the light from the scintillator so as to allow lock-in detection.

(5) Laser Induced Fluorescence of Impurities in Solid State Materials at Low Temperature

In Expt. XIII you investigated the room temperature (293 K) fluorescence spectrum of the uranyl ion UO22+ in autunite. The fluorescence peaks were found to have very large linewidths compared to those seen for free atoms such as hydrogen or mercury. These large linewidths were attributed to a strong coupling between the UO22+ ion and the thermal vibrations of the autunite crystal lattice. If this is indeed the case, what happens to the fluorescence spectrum at liquid helium (4 K) temperatures? Fig. 3(a) shows a laser induced fluorescence spectrum of the n' = 0 --> n = 0, 5015 Å transition in an autunite sample cooled to 4 K.14 It should be contrasted with the room temperature measurement of the same transition shown in Fig. 3(b), but familiar to you from its appearance as the leftmost fluorescence peak in Fig. 1. of Expt. XIII. The most striking feature of the 4 K spectrum is the complete absence of fluorescence corresponding to the short wavelength half of the peak seen at 293 K. This can be attributed to the near absence of lattice phonons at 4 K that can  add to the transition energy. The peaks to the right of so called "zero phonon" line in the 4 K spectrum correspond to energy loss to quantized modes of vibration of the autunite lattice.14

Required equipment includes:
(a) SPEX 1704 Spectrometer, data acquisition electronics, and IBM PC/XT computer,
(b) LN-1000 Nitrogen Gas Laser,
(c) Janus liquid helium research dewar with optical windows,
(d) delivery of liquid helium and liquid nitrogen,
(e) appropriate mineral samples.

(6) Raman Scattering

When intense, monochromatic light of frequency is directed at simple molecules such as O2, N2, CCl4, or CS2, it is found that the light scattered at right angles to the incident direction contains not only radiation of frequency , but also radiation at a group of frequencies 1', 2', ...., and N'.15,16,17 The energies h1', h2', ...., and hN' are found to correspond to energy differences between low lying vibrational or rotational states of the sample molecule. Thus, a scattered frequency - i' corresponds to absorption of energy by the molecule, whereas a scattered frequency + i' corresponds to a transfer of energy from the excited molecule to the scattered photon. The frequency shifts 1', 2', ...., and N' can be used to determine the shape of a molecule as well as the vibrational and rotational constants of molecular motion. The Raman effect is a scattering  process that involves a frequency change in the photon-molecule interaction without time delay.  This process is distinct from the fluorescence process observed for the uranyl ion in Expt. XIII where the emission of the fluorescence light occurs with finite (100 Ás) lifetime.

Required equipment includes:
(a) SPEX 1704 Spectrometer, data acquisition electronics, and IBM PC/XT computer,
(b) LN-1000 Nitrogen Gas Laser,
(c) ORTEC Model 408A Biased Amplifier,
(d) ORTEC Model 452 Spectroscopy Amplifier.

(7) Paschen-Back Effect in Atomic Mercury

The simple splittings observed in the spectra of Expt. XIV are characteristic of the Zeeman effect for small external magnetic fields. In sufficiently strong magnetic fields, the interaction of the electronic spin and orbital magnetic moments with the magnetic field becomes much greater than the internal spin-orbit interaction that couples the electronic spin and orbital motions.18,19 In the limit of very high external fields, the atomic fine structure states are said to be decoupled  in what is known as the Paschen-Back effect. The Paschen-Back effect of the 1P1 and 3P1 terms of atomic Hg has been measured in our laser spectroscopy laboratory.20,21 Fig. 4 shows the 5790.6 Å, 61D2 --> 61P1 transition of atomic Hg in a magnetic field of B = 23.8 kG. If you examine this spectrum closely, you should see at least three or four features that distinguish it from the highly symmetric Zeeman patterns obtained in Expt. XIV.

Required equipment includes:
(a) SPEX 1704 Spectrometer, data acquisition electronics and IBM PC/XT computer,
(b) Varian electromagnet,
(c) Hg lamp,
(d) Hall effect gaussmeter.

(8) Faraday Rotatiom

When monochromatic, linearly polarized light is passed through a transparent medium the direction of the linear polarization is ordinarily unchanged. However, when a large magnetic field parallel to the light direction is applied to the transmitting medium, there can be a large rotation of the polarization direction. This rotation, first detected by Faraday in 1845, depends linearly on the applied magnetic field strength B and a medium dependent parameter known as the Verdet constant.22,23 When plane mirrors are used to produce repeated passage of a light beam through the magnetic field region, the rotations of the individual passages are compounded. The Faraday rotation of a linearly polarized HeNe laser beam passing through distilled water has been measured in our optics laboratory.24 The wavelength dependence of the Verdet constant can be investigated using laser beams of different wavelength.

Required equipment includes:
(a) HeNe, GreNe, and HeCd lasers,
(b) high current solenoid with power supply,
(c) polarizers,
(d) Hall effect gaussmeter with longitudinal probe,
(e) cylindrical chamber with optical access ports,
(f) plane mirrors for multiple reflections.

(9) Double slit diffraction

Although you have seen the diffraction of HeNe laser light in lecture demonstrations, it is worthwhile to verify the interference pattern quantitatively in the laboratory. The theory of diffraction by single, double, and multiple finite slits is well understood and can be verified in detail with simple apparatus.25,26,27 The wavelength dependence of theoretical predictions can be tested using the three CW lasers available in our laboratories. One can also investigate the dependence of the interference pattern on the index of refraction of the medium following the slit arrangement.

Required equipment includes:
(a) HeNe, HeCd, and GreNe lasers,
(b) precision double slits,
(c) photodetector.

(10) Holography

In 1947, Dennis Gabor discovered a remarkable and Nobel Prize winning application of the interference property of light waves.28,29 By superimposing two sets of monochromatic and coherent wave fronts on a photographic plate (one set directed straight to the plate and the other reflected from an object onto the plate), a microscopic interference pattern is produced. The developed plate, called a "hologram", contains a permanent record of the interference pattern, i.e., it stores both amplitude and phase information. When the hologram is placed in a beam of the same coherent, monochromatic light, the beam is diffracted through the many fringes recorded on the hologram to produce a set of wavefronts identical to those originally reflected from the object. Consequently, when viewed, the diffracted wavefronts give a remarkably realistic, three-dimensional picture of the object.30,31,32

Required equipment includes:
(a) HeNe laser,
(b) photographic plates, plate holder,
(c) spatial filter,
(d) front surface mirrors,
(e) vibration-isolated optical bench,
(f) photographic developing equipment.

(11) High Temperature Superconductors

The recent discovery of superconductivity in the compound YBa2Cu33O7 has received considerable attention in the popular press and in scientific journals.33 In Expt. X you investigated magnetic levitation produced by a YBa2Cu33O7 sample made here at Middlebury. For your independent project you may wish to make additional samples. You should measure the resistivity of your samples near the transition temperature and also determine the critical fields of this type II superconductor. You can grind up a superconducting sample and reshape it to make a crude, cylindrical superconducting shield.

Required equipment includes:
(a) high temperature oven,
(b) IBM PC for oven control,
(c) Helmholtz coil assembly,
(d) liquid nitrogen,
(e) appropriate chemicals.
References
1. R. Eisberg and R. Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (John Wiley & Sons, New York, 1985), pp. 107-110.
2. P.A. Tipler, Modern Physics  (Worth Publishers, New York, 1978), pp. 155-156.
3. A. Melissinos, Experiments in Modern Physics  (Academic Press, New York, 1966), pp. 8-17.
4. Franck-Hertz Tube, manual (Klinger Educational Products, Jamaica, NY, 1982).
5. P.A. Tipler, ibid., pp. 96-102.
6. A. Melissinos, ibid., pp. 2-8.
7. R.A. Millikan, The Electron, 2nd ed. (University of Chicago Press, Chicago, 1924).
8. The Millikan Oil Drop Experiment, manual (PASCO Scientific, Lafeyette, CA, 1967).
9. Model 5300 Series Alpha Spectrometer, manual (The Nucleus, Oak Ridge, TN, 1979).
10. D.N. Jordan, Alpha-Gamma and Beta-Gamma Coincidence Emissions from 133Ba, 137Cs, and 228Th, B.A. thesis, Middlebury College, 1985.
11. R.D. Evans, The Atomic Nucleus  (Krieger, Malarbar, FL, 1982), pp. 517-519.
12. R.E. Lapp and H.L. Andrews, Nuclear Radiation Physics  (Prentice-Hall, Englewood Cliffs, NJ, 1972), pp. 45-54.
13. G.F. Knoll, Radiation Detection and Measurement  (John Wiley & Sons, New York, 1979), pp. 239-271.
14. R.S. Tucker, Laser Induced Fluorescence of the Uranyl Ion in Autunite at Liquid Nitrogen and Liquid Helium Temperatures, B.A. thesis, Middlebury College, 1987.
15. R. Eisberg and R. Resnick, ibid., pp. 432-434.
16. P.A. Tipler, ibid., p. 304.
17. D.P. Shoemaker, C.W. Garland, J.I. Steinfeld and J.W. Nibler, Experiments in Physical Chemistry, 4th ed. (McGraw-Hill, New York, 1981), pp. 427-438.
18. R. Eisberg and R. Resnick, ibid., p. 370.
19. P.A. Tipler, ibid., p. 277.
20. M.J. Kaufman, Zeeman and Paschen-Back Measurements in Atomic Mercury, B.A. thesis, Middlebury College, 1987.
21. T.D. Donnelly, Intermediate Coupling and the Paschen-Back Effect in Atomic Mercury, B.A. thesis, Middlebury College, 1990.
22. Handbook of Optics, edited by W.G. Driscoll and W. Vaughan (McGraw-Hill, New York, 1978), Chap. 17, pp. 20-21.
23. Encyclopedia of Physics, edited by R.G. Lerner and G.L. Trigg (Addison-Wesley, Reading, MA, 1981), pp. 296-297.
24. K.A. Datar, The Optical Faraday Effect, B.A. thesis, Middlebury College, 1991.
25. D. Halliday and R. Resnick, Fundamentals of Physics, 2nd ed. (John Wiley & Sons, New York, 1981), pp. 747-758.
26. G.R. Fowles, Introduction to Modern Optics  (Holt, Rinehart and Winston, New York, 1968), pp. 106-125.
27. R.S. Sirohi, A Course of Experiments with He-Ne Laser  (Halstead Press, New Delhi, 1985).
28. N. Abramson, The Making and Evaluation of Holograms  (Academic Press, London, 1981).
29. T. Kalland, Exploring Laser Light  (American Association of Physics Teachers, New York, 1977), pp. 221-267.
30. H.J. Schmidt, Holograms of Holographic Images, B.A. thesis, Middlebury College, 1981.
31. M.L. Rich, Time Average Holographic Interferometry: Separable Motion and Multiple Modes, B.A. thesis, Middlebury College, 1984.
32. K. Lubell, Real Time Holographic Interferometry, B.A. thesis, Middlebury College, 1985.
33. M.K. Wu, J.R. Ashburn, C.J. Torng, P.H. Hor, R.L. Meng, L. Gao, Z.J. Huang, Y.Q. Wang, and C.W. Chu, Phys. Rev. Lett., Vol. 58, 908 (1987).

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