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UNIT 25 : WAVE PROPERTIES OF PARTICLE (2 Hours)

is a phenomenon where under certain circumstances a particle exhibits wave properties and under other conditions a wave exhibits properties of a particle. UNIT 25 : WAVE PROPERTIES OF PARTICLE (2 Hours). 25.1 The de Broglie wavelength 25.2 Electron diffraction.

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UNIT 25 : WAVE PROPERTIES OF PARTICLE (2 Hours)

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  1. is a phenomenon where under certain circumstances a particle exhibits wave properties and under other conditions a wave exhibits properties of a particle. UNIT 25 : WAVE PROPERTIES OF PARTICLE (2 Hours) 25.1 The de Broglie wavelength 25.2 Electron diffraction

  2. 25.1 The de Broglie wavelength (1 Hour) At the end of this topic, students should be able to: • State wave-particle duality • Use de Broglie wavelength,

  3. Introduction Classical Physics - Deals with 2 categories of phenomena (a) Particles -- tiny objects like bullets, electron, proton, neutron. -- they have mass & obey Newton’s Laws. (b) Waves -- travels through an opening or around a barrier the wave diffracts & different parts of the wave interfere. -- both have properties that are mutually exclusive.

  4. 25.1 The de Broglie wavelength Wave-Particle Dualityis the phenomenon where under certain circumstances a particle exhibits waveproperties, and under other conditions a wave exhibits properties of a particle. But we cannot observe both aspect of its behavior simultaneously,

  5. According to the Quantum theory, a photon of electromagnetic radiation of wavelength λ has energy : ….(1) where h : Planck constant c : speed of light in vacuum

  6. According to Einstein’s Theory of special relativity, the energy equivalent E of a mass m is given by: Equating (1) & (2):

  7. 10.1 The de Broglie wavelength • So, the momentum p of a photon with wavelength λ • is given by and De broglie wavelength property of wave property of particle

  8. Evidences to show duality of light can behave as Particle behaves as a wave Electron diffraction

  9. Example 25.1.1 In a photoelectric effect experiment, a light source of wavelength 5 x 10-7 m is incident on a potassium surface. Calculate the momentum and energy of the photon used. (Planck’s constant, h = 6.63 x 10-34 J s)

  10. Example 25.1.2 Calculate the de- broglie wavelength for : (a) A car of mass 2x 103 kg moving at 50 ms -1. (b) An electron of mass 9.11x10-31 kg moving at 1x108 m s-1. Solution

  11. Example 25.1.3 An electron and a photon has the same wavelength of 0.25 nm. Calculate the momentum and energy (in eV) of the electron and the photon. For an electron :

  12. Solution 25.1.3 For a photon :

  13. Exercise 1. In a photoelectric effect experiment, a light source of wavelength 550 nm is incident on a sodium surface. Determine the momentum and the energy of a photon used. (Given the speed of light in the vacuum, c =3.00108 m s1 and Planck’s constant, h =6.631034 J s)

  14. Exercise 2. An electron and a proton have the same speed. a. Which has the longer de Broglie wavelength? Explain. b. Calculate the ratio of e/ p. (Given c =3.00108 m s1, h =6.631034 J s, me=9.111031 kg, mp=1.671027 kg and e=1.601019 C) ( )

  15. Solution : From de Broglie relation, the de Broglie wavelength is inversely proportional to the mass of the particle. Since the electron lighter than the mass of the proton therefore the electron has the longer de Broglie wavelength.

  16. Solution :

  17. 25.2 Electron Diffraction(1 Hour) At the end of this topic, students should be able to: • Describe the observations of electron diffraction in Davisson-Germer experiment. • Explain the wave behaviour of electron in an electron microscope. • State the advantages of electron microscope compared to optical microscope.

  18. diffraction pattern graphite film screen anode e +4000 V cathode electron diffraction Electron diffraction tube 25.2 Electron diffraction

  19. The figure show the Davisson-Germer to discover electron diffraction.

  20. 25.2 Electron diffraction • In 1927 , two physicists C.J Davission and L. H • Germer carried out electron diffraction experiment • to prove the de Broglie relationship. • A graphite film is used as a target. • A beam of electrons in a cathode-ray tube is • accelerated by the applied voltage towards a • graphite film. • The beam of electrons is diffracted after passing • through the graphite film. • A diffraction pattern is observed on the fluorescence • screen. • This shows that a beam of fast moving particles • (electrons) behaves as a wave, exhibiting diffraction • – a wave property.

  21. 25.2 Electron diffraction 25.2 Electron diffraction • Davisson and Germer discovered that if the • velocity of electrons is increased, the rings are • seen to become narrower showing that the • wavelength of electrons decreases with • increasing velocity as predicted by de Broglie • relationship. ….(1)

  22. The velocity of electronscan be determined • from the accelerating voltage (voltage between anode and cathode) i.e : ….(2) (2) into (1) , V = accelerating voltage

  23. Example 25.2.3 An electron is accelerated from rest through a potential difference of 1200 V. Calculate its de Broglie wavelength. (me= 9.11 x 10-31 kg)

  24. Example 25.2.4 An electron and a proton have the same kinetic energy. Determine the ratio of the de Broglie wavelength of the electron to that of the proton. (me= 9.11 x 10-31 kg, mp = 1.67 x 10-27 kg)

  25. Exercise An electron and a photon has the same wavelength of 0.21 nm. Calculate the momentum and energy (in eV) of the electron and the photon.

  26. Electron Microscope • A practical devicethat relies on the wave • properties of electrons is electron microscope. • It is similar to optical compound microscope in many aspects. • The advantage of the electron microscope over • the optical microscope is the resolving powerof • the electron microscopeis much higherthan that of an optical microscope. The resolving poweris inversely proportional to the wavelength- a smaller wavelength means greater resolving power, or the ability to see details.

  27. Electron Microscope • This is because the electrons can be accelerated to a very high kinetic energy (KE) giving them a very short wavelengthλ typically 100 times shorter than those of visible light. • As a result, electron microscopes are able to • distinguish details about 100 times smaller. - Thus, an electron microscope can distinguish clearly 2 points separated by a distance which is of the order of nanometer. - But an compound microscope can only distinguish clearly 2 points separated by a distance which is of order of micrometer.

  28. Electron Microscope • In the electron microscope, electrons are produced • by the electron gun. • Electrons are accelerated by voltages on the order of • 105 V have wavelengths on the order of 0.004 nm. • Electrons are deflected by the “magnetic lens” to • form a parallel beam which then incident on the • object. • The “magnetic lens” are actually magnetic fields that • exert forces on the electrons to bring them to a • focus. • The fields are produced by carefully designed • current-carrying coils of wire.

  29. Electron Microscope • When the object is struck by the electrons, more penetrate in some parts than in others, depending on the thickness and density of the part. • The image is formed on a fluorescent screen. • The image is brightest where most electrons have been transmitted. The object must be very thin, otherwise too much electron scattering occurs and no image form.

  30. Electron Microscope • Two types of electron microscope : a) transmission electron microscope, which produces a two-dimensional image. b) scanning electron microscope, which produces a three-dimensional image.

  31. Transmission Electron Microscope

  32. Scanning Electron Microscope

  33. Fig 40-17, p.1303

  34. A mite – maximum length = 0.75 mm Fig 40-18, p.1304

  35. Fig 41-12, p.1340

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