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Wave behaviour of particles 07


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SACE Physics Section 3 Topic 4

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Wave behaviour of particles 07

  2. 2. WAVE BEHAVIOUR OF PARTICLES <ul><li>In the previous topics, it was shown that in some circumstances, light exhibits certain behaviours characteristic of waves. </li></ul><ul><li>In other circumstances, light behaves as particles. </li></ul><ul><li>Could the reverse be true, namely that particles can behave as waves ? This topic investigates this question. </li></ul>
  3. 3. WAVE BEHAVIOUR OF PARTICLES <ul><li>DE BROGLIE’S HYPOTHESIS </li></ul><ul><li>Count Louis de Broglie (1892 - 1970) believed in the symmetry of nature. In 1923 he reasoned that if a photon could behave like a particle, then a particle could behave as a wave. </li></ul>
  4. 4. WAVE BEHAVIOUR OF PARTICLES <ul><li>He turned Compton’s relationship to make wavelength the subject of the equation. </li></ul><ul><li>Compton- “a photon has momentum” </li></ul><ul><li>De Broglie- “An electron has a wavelength” </li></ul>
  5. 5. WAVE BEHAVIOUR OF PARTICLES <ul><li>This is called the de Broglie wavelength of a particle. </li></ul><ul><li>All particles (electrons, protons, bullets, even humans) have a wavelength. </li></ul><ul><li>They must be moving. </li></ul><ul><li>They are called “matter waves”. </li></ul>
  6. 6. WAVE BEHAVIOUR OF PARTICLES <ul><li>We cannot see light. We can only make inferences about the nature of light by looking at its properties. </li></ul><ul><li>Its properties indicate that it is both wave like and particle like in nature. </li></ul>
  7. 7. WAVE BEHAVIOUR OF PARTICLES <ul><li>We also cannot see atoms. We often think of them as exhibiting the properties of particles. </li></ul><ul><li>But, because we have never seen them, could they be waves pretending to be particles? </li></ul><ul><li>De Broglie suggested that particles, in some instances could be wave like. </li></ul>
  8. 8. EXAMPLE 1 <ul><li>Calculate the de Broglie wavelength associated with a 1.0 kg mass fired through the air at 100 km/hr. </li></ul>
  10. 10. EXAMPLE 1 SOLUTION <ul><li>Note the wavelength is so small that it cannot be detected and measured. </li></ul><ul><li>We cannot create slits capable of diffracting such small wavelengths. </li></ul><ul><li>Can a microscopic object give a more realistic wavelength? </li></ul>
  11. 11. EXAMPLE 2 <ul><li>Calculate the de Broglie wavelength that would be associated with an electron accelerated from rest by a P.D. of 9.0V </li></ul>
  14. 14. WAVE BEHAVIOUR OF PARTICLES <ul><li>An electron creates a larger wavelength than a macroscopic object due to the fact that it has a very small mass. </li></ul><ul><li>The wavelength of an electron is very similar to the wavelength of an x-ray. </li></ul><ul><li>A beam of electrons should then be able to be diffracted, proving that they have wave like properties. </li></ul>
  15. 15. WAVE BEHAVIOUR OF PARTICLES <ul><li>This wavelength can be measured using a crystal diffraction grating as mentioned previously as the spacing of the atoms in the crystal is in the order of 10 -10 m. </li></ul><ul><li>These waves are not caused by the particle but are connected with its motion. </li></ul>
  16. 16. WAVE BEHAVIOUR OF PARTICLES <ul><li>The wavelengths are 1000 x smaller than visible light. </li></ul><ul><li>Electron beams in electron microscopes are used as they have </li></ul><ul><ul><li>greater resolving powers and </li></ul></ul><ul><ul><li>hence greater magnification. </li></ul></ul>
  17. 17. EXAMPLE 3 <ul><li>Calculate the de Broglie  of a H atom moving at 158 m s -1 (interstellar space) </li></ul>
  18. 18. EXAMPLE 3 SOLUTION  = 2.50 x 10 -9 m These are X Rays which do not penetrate the atmosphere
  19. 19. DAVISSON-GERMER EXPERIMENT <ul><li>C.J. Davisson and L.H. Germer performed an experiment to verify de Broglie’s hypothesis. </li></ul>
  20. 20. DAVISSON-GERMER EXPERIMENT <ul><li>Electrons were allowed to strike a nickel crystal. The intensity of the scattered electrons is measured for various angles for a range of accelerating voltages. </li></ul>
  22. 22. DAVISSON-GERMER EXPERIMENT <ul><li>It was found that a strong ‘reflection’ was found at θ = 50° when V = 54V. </li></ul><ul><li>This appeared to be a place of constructive interference, suggesting that the “matter waves” from the electrons were striking the crystal lattice and diffracting into an interference pattern. </li></ul>
  23. 23. DAVISSON-GERMER EXPERIMENT <ul><li>The interatomic spacing of Nickel is close to the ‘wavelength’ of an electron. Therefore it would seem possible that electron matter waves could be diffracted. </li></ul><ul><li>Davisson and Germer set out to verify that the electrons were behaving like a wave using the following calculations. </li></ul>
  24. 24. DAVISSON-GERMER EXPERIMENT <ul><li>Theoretical Result (according to de Broglie’s calculation) </li></ul><ul><li>The kinetic energy of the electrons is </li></ul><ul><li>1/2 mv 2 = Ve </li></ul><ul><li>So mv = </li></ul>
  25. 25. DAVISSON-GERMER EXPERIMENT <ul><li>The de Broglie wavelength is given by: </li></ul><ul><li>For this experiment: </li></ul>
  26. 26. DAVISSON-GERMER EXPERIMENT <ul><li>This is de Broglie’s theoretical calculaton of what the wavelength should be if a particle were to behave like a wave. </li></ul>
  27. 27. DAVISSON-GERMER EXPERIMENT <ul><li>Experimental Result (according to Davisson-Germer) </li></ul><ul><li>X-ray diffraction had already shown the interatomic distance was 0.215 nm for nickel. </li></ul><ul><li>Since θ = 50° , the angle of incidence to the reflecting crystal planes in the nickel crystal is 25 ° as shown below: </li></ul>
  29. 29. DAVISSON-GERMER EXPERIMENT <ul><li>dsin θ = mλ </li></ul><ul><li>For the first order reinforcement… </li></ul><ul><li>λ = dsinθ </li></ul><ul><li>= (.215 x 10 -9 )(sin50°) </li></ul><ul><li>= 1.65 x 10 -10 m </li></ul>
  30. 30. DAVISSON-GERMER EXPERIMENT <ul><li>The close correspondence between the theoretical prediction for the wavelength by de Broglie ( 1.67 x 10 -10 m) and the experimental results of Davisson-Germer ( 1.65 x 10 -10 m) provided a strong argument for the de Broglie hypothesis. </li></ul>
  31. 31. APPLICATION – ELECTRON MICROSCOPES <ul><li>LIGHT MICROSCOPES </li></ul><ul><li>A normal light microscope is based on at least two converging lenses, the objective and the eyepiece. </li></ul><ul><li>There is a limit to how much the conventional microscope can magnify the image. This is due to diffraction. </li></ul>
  32. 32. APPLICATION – ELECTRON MICROSCOPES <ul><li>This determines the minimum distance between two points on the object that can be distinguished as separate. </li></ul><ul><li>Instead of coming to a focus at a point, the light focuses to a small disc. Any attempt to increase the magnification just magnifies the diffraction disc. </li></ul>
  33. 33. APPLICATION – ELECTRON MICROSCOPES <ul><li>For light microscopy, the minimum distance, using light of wavelength of about 5 x 10 -7 m, is about 2 x 10 -7 m. </li></ul><ul><li>This corresponds to a magnification of about 1000. Using ultraviolet light, the magnification can be increased </li></ul><ul><li>to 3000 x. </li></ul>
  34. 34. APPLICATION – ELECTRON MICROSCOPES <ul><li>X-rays have smaller wavelengths and so could be considered for use. </li></ul><ul><li>The problem is that they do not refract significantly and are unsuitable for conventional microscopes, as they cannot be focused easily. </li></ul>
  36. 36. APPLICATION – ELECTRON MICROSCOPES <ul><li>Once the wavelike properties of electrons were discovered, people realised that they had the properties that were required for high magnification; 1) they have a small wavelength and 2) they can be focused using electric or magnetic fields. </li></ul>
  37. 37. APPLICATION – ELECTRON MICROSCOPES <ul><li>Just as an X-ray tube can produce electrons, electrons can be produced for an electron microscope in the same manner by accelerating of electrons across a large P.D. </li></ul><ul><li>This takes place in an electron gun with P.D.’s in the range of 40 kV to 100 kV. </li></ul>
  38. 38. APPLICATION – ELECTRON MICROSCOPES <ul><li>The work done by the electric field and assuming the electrons start from rest, their kinetic energy is given by q  V . </li></ul><ul><li>In the case where the accelerating potential is 60 KV, the kinetic energy is: </li></ul><ul><li>K = q  V = (1.6 x 10 -19 ) x (60 x 10 3 ) = 9.60 x 10 -15 J. </li></ul>
  39. 39. APPLICATION – ELECTRON MICROSCOPES <ul><li>To determine the wavelength of the electrons, the de Broglie relationship is used,  = h / p . </li></ul><ul><li>The momentum must first be determined from the kinetic energy: </li></ul><ul><li>K = ½mv 2 = ½m 2 v 2 /m = p 2 /2m </li></ul>
  40. 40. APPLICATION – ELECTRON MICROSCOPES <ul><li>And so the momentum can be determined by: </li></ul><ul><li>P = </li></ul><ul><li>= </li></ul><ul><li> P = 1.32 x 10 -22 kgms -1 </li></ul>
  41. 41. APPLICATION – ELECTRON MICROSCOPES <ul><li> = h / p = 6.63 x 10 -34 /1.32 x 10 -22 = </li></ul><ul><li> = 5.01 x 10 -12 m </li></ul><ul><li>This value is about 100 000 times smaller than visible light. </li></ul><ul><li>This makes it easier to distinguish between two points that are separated by only 1 x 10 -10 m and have useful magnifications of over 1 million. The problem remains how to focus them. </li></ul>
  42. 42. APPLICATION – ELECTRON MICROSCOPES <ul><li>In a Transmission Electron Microscope (TEM), the electron gun replaces the lamp and electrostatic lenses (usually magnetic lenses) replace the optical lens. </li></ul><ul><li>The electron image is converted to visible light on a fluorescent screen. The electrostatic lens is shown below: </li></ul>
  44. 44. APPLICATION – ELECTRON MICROSCOPES <ul><li>A parallel beam of electrons that enters the lens along any line except the central vertical axis, experiences a force due to the electric field that deflects them toward the central axis. </li></ul><ul><li>Their paths are such that all electrons reach this central axis at the same distance from the lens. This is the focal length of the lens. </li></ul>
  45. 45. APPLICATION – ELECTRON MICROSCOPES <ul><li>A magnetic lens is shown below: </li></ul>
  46. 46. APPLICATION – ELECTRON MICROSCOPES <ul><li>The result of using this lens is the same as the electrostatic lens but the path of the electrons is a little more complicated. </li></ul><ul><li>At any instant, the motion of the electron can be resolved into components parallel and perpendicular to the field. </li></ul>
  47. 47. APPLICATION – ELECTRON MICROSCOPES <ul><li>For a field that is correctly shaped with the appropriate magnitude, the original parallel beam can come together along the central axis at a fixed distance that is the focal length of the lens. </li></ul><ul><li>In present day electron microscopes, magnetic lenses have virtually replaced electrostatic lenses. </li></ul>
  48. 48. APPLICATION – ELECTRON MICROSCOPES <ul><li>To recap… electron microscopes can focus on smaller objects due to the fact that an electron has a smaller wavelength than visible light. </li></ul><ul><li>The electron can also be focused using electric and magnetic fields. </li></ul><ul><li>We use the ability of an electron (particle) to behave like a wave in the use this technology. </li></ul>
  49. 49. APPLICATION – ELECTRON MICROSCOPES <ul><li>Scanning Electron Microscope </li></ul>
  50. 50. APPLICATION – ELECTRON MICROSCOPES <ul><li>Hard Disc </li></ul>
  51. 51. APPLICATION – ELECTRON MICROSCOPES <ul><li>Ant holding a microchip </li></ul>
  52. 52. APPLICATION – ELECTRON MICROSCOPES <ul><li>DNA </li></ul>