Chapter 10: Wave Properties of Particles

Size: px

Start display at page:

Download "Chapter 10: Wave Properties of Particles"

Philip Sparks
6 years ago
Views:

properties to produce magnified images of

1 Chapter 10: Wave Properties of Particles Particles such as electrons may demonstrate wave properties under certain conditions. The electron microscope uses these properties to produce magnified images of minute objects that could not be produced by optical microscope.

2 Overview Wave Properties of Particles De Broglie Wavelength Electron Diffraction

3 10.1 The de Broglie Wavelength State wave-particle duality. Use de Broglie wavelength, h p Learning Objectives

4 The de Broglie Wavelength Wave-particle duality is the phenomenon where under certain circumstances a particle exhibits wave properties, and under other conditions a wave exhibits properties of a particle. But we cannot observe both aspect of its behaviour simultaneously. According to the Planck s quantum theory, a photon of electromagnetic radiation of wavelength λ has energy: E hc hf (1)

5 The de Broglie Wavelength According to Einstein s theory of special relativity, the energy equivalent E of a mass m is given by 2 E mc (2) Since momentum p = mc, the equation can also be written as E = pc. By equating (1) and (2): hc pc Properties of wave h p Properties of particle De Broglie Wavelength

6 The de Broglie Wavelength Evidences to show duality of light: Light can behave as Particle Photoelectric Effect Compton effect Wave Young s Double Slit experiment Diffraction grating experiment

7 The de Broglie Wavelength Evidences to show duality of particle: Particle can behave as a wave Electron Diffraction (Davisson-Germer Experiment)

8 Example 1 Calculate the de Broglie wavelength for : a. A car of mass kg moving at 50 m s -1 b. An electron of mass kg moving at m s -1 (Given the speed of photon in the vacuum, c = m s -1 and Planck constant, h = J s)

9 Example 1 Solution

10 Example 2 In a photoelectric effect experiment, a light source of wavelength 500 nm is incident on a potassium surface. Find the momentum and energy of a photon used. (Given the speed of photon in the vacuum, c = m s -1 and Planck constant, h = J s)

11 Example 2 Solution

12 Davisson-Germer Experiment Electron diffraction tube

13 Davisson-Germer Experiment 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.

14 Davisson-Germer Experiment This shows that a beam of fast moving particles (electrons) behaves as a wave, exhibiting diffraction a wave property. 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. h mv, v,

15 Davisson-Germer Experiment The velocity of electrons can be determined from the accelerating voltage (voltage between anode and cathode): U K ev 1 mv 2 2 v 2eV m By substituting equation above into de Broglie relation: h 2meV

16 Example 3 An electron is accelerated from rest through a potential difference of 1200 V. Calculate its de Broglie wavelength. (Given c = m s 1, h = J s, m e = kg and e = C)

17 Example 3 Solution

18 Example 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.

19 Example 4 Solution

20 Electron Microscope A practical device that 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 power of the electron microscope is much higher than that of an optical microscope. The resolving power is inversely proportional to the wavelength - a smaller wavelength means greater resolving power, or the ability to see details.

21 Electron Microscope This is because the electrons can be accelerated to a very high kinetic energy (KE) giving them a very short wavelength λ 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 a compound microscope can only distinguish clearly 2 points separated by a distance which is of order of micrometer.

22 Electron Microscope There are two types of electron microscopes: Transmission produces a two-dimensional image. Scanning produces images with a threedimensional quality.

23 Wave Behaviour of Electron in an Electron Microscope 1. In the electron microscope, electrons are produced by the electron gun. 2. Electrons are accelerated by voltages on the order of 10 5 V have wavelengths on the order of nm. 3. Electrons are deflected by the magnetic lens to form a parallel beam which then incident on the object. 4. The magnetic lens is actually magnetic fields that exert forces on the electrons to bring them to a focus. The fields are produced by carefully designed currentcarrying coils of wire.

24 Wave Behaviour of Electron in an Electron Microscope 5. 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. 6. 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.

25 Example 5 Why can an electron microscope resolve smaller objects than a light microscope?

26 Example 5 Solution An electron microscope resolve smaller objects than a light microscope because the electrons can be accelerated to a very high kinetic energy (KE) giving them a very short wavelength λ typically 100 times shorter than those of visible light. Since the resolving power is inversely proportional to the wavelength, wavelength, resolving power Therefore electron microscopes are able to distinguish details about 100 times smaller than optical microscope.

λ = h = h p mv λ = h mv FXA 2008 Candidates should be able to :

λ = h = h p mv λ = h mv FXA 2008 Candidates should be able to : 1 Candidates should be able to : Explain electron diffraction as evidence for the wave nature of particles like electrons. Explain that electrons travelling through polycrystalline graphite will be diffracted