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120 CHAPTER 9. ELECTRON SPIN RESONANCE Connect the RF unit to the power supply, place the sample in the center of the coil. Position the RF coil as centrally as possible into the Helmholtz coils. After everything is connected examine the voltage across the resistor and the current through the RF unit simultaneously. Adjust the current through the coils. What happens to the current through the RF unit? Question (c): Why do the features on the plot change? Discuss with your demonstrator. You should now be able to determine how best to measure B when resonance occurs. Question (d): How should the maximum current through the coils be chosen such that you reduce the error when measuring B at resonance? Measure the voltage at which resonance occurs, as a function of RF frequency. Use the small bar magnet to observe any changes when you change the magentic field by placing the magnet near the sample such that it is parallel and then perpendicular to the coil axis. Explain. Question (e): You should have enough information to determine g s . How does it compare to the nominal g s = 2? Question (f): Why to we observe a width on the resonance peak? 9.7 Extension: electron diffraction This section contains some extra work for efficient or ambitious students. It should only be attempted when all the work in the previous section has been completed. You can still get full marks having done only the previous section. 9.7.1 Overview The postulate that matter may also possess wave-like properties was one of the most stunning and unifying hypotheses of this century. In 1924 de Broglie, working from arguments based on the properties of wave packets, hazarded that the wavelength of these matter waves could be obtained from the same relationship that held for light, namely λ = h p (9.9) where λ is the wavelength, p is the momentum and h is Planck’s constant 1 . Davisson and Germer obtained the first experimental evidence for matter waves by reflecting slow electrons from the face of a single nickel crystal. The wavelength that they were able to 1 Some useful data, including a value for h, are provided in section 9.8.
9.7. EXTENSION: ELECTRON DIFFRACTION 121 determine from using the periodic array of nickel atoms as a diffraction grating was strikingly similar to that calculated from the de Broglie relation. Further experimentation by Thomson yielded diffraction patterns from the transmission of electrons through thin polycrystalline foils. The fact that non-relativistic electron wavelengths are comparable to interatomic distances in solids means that electron diffraction experiments (such as Transmission Electron Microscopy, or TEM) are powerful probes of the structure of solids. 9.7.2 Basic theory 9.7.2.1 Wavelength The wavelength of a beam of electrons is given by λ = h p = h mv . (9.10) Thus in the non-relativistic limit the wavelength is inversely proportional to the electron velocity v. Conservation of energy requires that for a charge accelerated through a potential the change in kinetic energy plus the change in electrical potential energy while traversing from one point to another must equal zero. Thus we may write ( ) mv 2 2 2 + mv2 1 + (eV 2 − eV 1 ) = 0 (9.11) 2 where V 1 and V 2 are the potentials at points 1 and 2 respectively. Applied to the electron transversing an electron gun in an electron diffraction tube V 2 is V a , the anode voltage and V 1 equals zero. So for negative charges mv 2 2 = eV a . (9.12) Hence the wavelength is given by λ = h √ 2meVa , (9.13) where m and e are the mass and charge of the electron respectively. When the values of the constants are substituted into equation 9.13 and the potential is in volts then the wavelength in nanometres is given by λ = 1.2264 √ Va . (9.14)
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ii CONTENTS 3 The Michelson interfe
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iv CONTENTS 6.1 Introduction . . .
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vi CONTENTS 9.3.1 Orbital Angular M
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viii CONTENTS 13 Energy loss of α
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Chapter 1 Introduction The experime
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1.2. EXPERIMENTAL TECHNIQUES 3 1.2
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1.3. THE REPORT 5 - Show quantities
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Chapter 2 2-slit interference with
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2.3. APPARATUS 17 Light sources Dou
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2.4. EXPERIMENT - LASER 19 the filt
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Chapter 4 Fraunhofer diffraction 4.
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4.3. THEORY 35 X Σ σ P d/2 dx R
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4.4. EXPERIMENT 39 Question 4.3 Doe
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4.4. EXPERIMENT 41 where F(x) = sin
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4.6. APPENDICES 45 • An intensity
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Chapter 5 Holography 5.1 Abstract H
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5.4. BACKGROUND 49 photography is a
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5.5. EXPERIMENT 53 than it takes to
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5.6. APPENDICES 55 Once you have se
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BIBLIOGRAPHY 57 Bibliography [1] E
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Chapter 6 Magnets And magnetic fiel
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6.3. THE HALL EFFECT 63 We now assi
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6.4. EXPERIMENT 65 Question 6.4 Wha
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170 CHAPTER 13. ENERGY LOSS OF α P
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Chapter 14 Errors 14.1 Introduction
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14.3. GRAPHS AND ERRORS 179 14.3 Gr
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14.4. EXCEL 181 technique was devel
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188 CHAPTER 15. EXCEL TUTORIAL ADC
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190 CHAPTER 15. EXCEL TUTORIAL Figu
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Chapter 16 The Safe Use of Lasers 1
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Multiplier Prefix Symbol 10 −24 y
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Bibliography - School of Physics - University of Melbourne

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