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SACE Physics Section 3 Topic 4

SACE Physics Section 3 Topic 4

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    Wave behaviour of particles 07 Wave behaviour of particles 07 Presentation Transcript

    • WAVE BEHAVIOUR OF PARTICLES 12 SACE PHYSICS-STAGE 2 SECTION 3 TOPIC 4 PRINCE ALFRED COLLEGE
    • WAVE BEHAVIOUR OF PARTICLES
      • In the previous topics, it was shown that in some circumstances, light exhibits certain behaviours characteristic of waves.
      • In other circumstances, light behaves as particles.
      • Could the reverse be true, namely that particles can behave as waves ? This topic investigates this question.
    • WAVE BEHAVIOUR OF PARTICLES
      • DE BROGLIE’S HYPOTHESIS
      • 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.
    • WAVE BEHAVIOUR OF PARTICLES
      • He turned Compton’s relationship to make wavelength the subject of the equation.
      • Compton- “a photon has momentum”
      • De Broglie- “An electron has a wavelength”
    • WAVE BEHAVIOUR OF PARTICLES
      • This is called the de Broglie wavelength of a particle.
      • All particles (electrons, protons, bullets, even humans) have a wavelength.
      • They must be moving.
      • They are called “matter waves”.
    • WAVE BEHAVIOUR OF PARTICLES
      • We cannot see light. We can only make inferences about the nature of light by looking at its properties.
      • Its properties indicate that it is both wave like and particle like in nature.
    • WAVE BEHAVIOUR OF PARTICLES
      • We also cannot see atoms. We often think of them as exhibiting the properties of particles.
      • But, because we have never seen them, could they be waves pretending to be particles?
      • De Broglie suggested that particles, in some instances could be wave like.
    • EXAMPLE 1
      • Calculate the de Broglie wavelength associated with a 1.0 kg mass fired through the air at 100 km/hr.
    • EXAMPLE 1 SOLUTION
    • EXAMPLE 1 SOLUTION
      • Note the wavelength is so small that it cannot be detected and measured.
      • We cannot create slits capable of diffracting such small wavelengths.
      • Can a microscopic object give a more realistic wavelength?
    • EXAMPLE 2
      • Calculate the de Broglie wavelength that would be associated with an electron accelerated from rest by a P.D. of 9.0V
    • EXAMPLE 2 SOLUTION
    • EXAMPLE 2 SOLUTION
    • WAVE BEHAVIOUR OF PARTICLES
      • An electron creates a larger wavelength than a macroscopic object due to the fact that it has a very small mass.
      • The wavelength of an electron is very similar to the wavelength of an x-ray.
      • A beam of electrons should then be able to be diffracted, proving that they have wave like properties.
    • WAVE BEHAVIOUR OF PARTICLES
      • 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.
      • These waves are not caused by the particle but are connected with its motion.
    • WAVE BEHAVIOUR OF PARTICLES
      • The wavelengths are 1000 x smaller than visible light.
      • Electron beams in electron microscopes are used as they have
        • greater resolving powers and
        • hence greater magnification.
    • EXAMPLE 3
      • Calculate the de Broglie  of a H atom moving at 158 m s -1 (interstellar space)
    • EXAMPLE 3 SOLUTION  = 2.50 x 10 -9 m These are X Rays which do not penetrate the atmosphere
    • DAVISSON-GERMER EXPERIMENT
      • C.J. Davisson and L.H. Germer performed an experiment to verify de Broglie’s hypothesis.
    • DAVISSON-GERMER EXPERIMENT
      • 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.
    • DAVISSON-GERMER EXPERIMENT
    • DAVISSON-GERMER EXPERIMENT
      • It was found that a strong ‘reflection’ was found at θ = 50° when V = 54V.
      • 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.
    • DAVISSON-GERMER EXPERIMENT
      • 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.
      • Davisson and Germer set out to verify that the electrons were behaving like a wave using the following calculations.
    • DAVISSON-GERMER EXPERIMENT
      • Theoretical Result (according to de Broglie’s calculation)
      • The kinetic energy of the electrons is
      • 1/2 mv 2 = Ve
      • So mv =
    • DAVISSON-GERMER EXPERIMENT
      • The de Broglie wavelength is given by:
      • For this experiment:
    • DAVISSON-GERMER EXPERIMENT
      • This is de Broglie’s theoretical calculaton of what the wavelength should be if a particle were to behave like a wave.
    • DAVISSON-GERMER EXPERIMENT
      • Experimental Result (according to Davisson-Germer)
      • X-ray diffraction had already shown the interatomic distance was 0.215 nm for nickel.
      • Since θ = 50° , the angle of incidence to the reflecting crystal planes in the nickel crystal is 25 ° as shown below:
    • DAVISSON-GERMER EXPERIMENT
    • DAVISSON-GERMER EXPERIMENT
      • dsin θ = mλ
      • For the first order reinforcement…
      • λ = dsinθ
      • = (.215 x 10 -9 )(sin50°)
      • = 1.65 x 10 -10 m
    • DAVISSON-GERMER EXPERIMENT
      • 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.
    • APPLICATION – ELECTRON MICROSCOPES
      • LIGHT MICROSCOPES
      • A normal light microscope is based on at least two converging lenses, the objective and the eyepiece.
      • There is a limit to how much the conventional microscope can magnify the image. This is due to diffraction.
    • APPLICATION – ELECTRON MICROSCOPES
      • This determines the minimum distance between two points on the object that can be distinguished as separate.
      • 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.
    • APPLICATION – ELECTRON MICROSCOPES
      • For light microscopy, the minimum distance, using light of wavelength of about 5 x 10 -7 m, is about 2 x 10 -7 m.
      • This corresponds to a magnification of about 1000. Using ultraviolet light, the magnification can be increased
      • to 3000 x.
    • APPLICATION – ELECTRON MICROSCOPES
      • X-rays have smaller wavelengths and so could be considered for use.
      • The problem is that they do not refract significantly and are unsuitable for conventional microscopes, as they cannot be focused easily.
    • APPLICATION – ELECTRON MICROSCOPES
      • ELECTRON MICROSCOPES:
    • APPLICATION – ELECTRON MICROSCOPES
      • 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.
    • APPLICATION – ELECTRON MICROSCOPES
      • 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.
      • This takes place in an electron gun with P.D.’s in the range of 40 kV to 100 kV.
    • APPLICATION – ELECTRON MICROSCOPES
      • The work done by the electric field and assuming the electrons start from rest, their kinetic energy is given by q  V .
      • In the case where the accelerating potential is 60 KV, the kinetic energy is:
      • K = q  V = (1.6 x 10 -19 ) x (60 x 10 3 ) = 9.60 x 10 -15 J.
    • APPLICATION – ELECTRON MICROSCOPES
      • To determine the wavelength of the electrons, the de Broglie relationship is used,  = h / p .
      • The momentum must first be determined from the kinetic energy:
      • K = ½mv 2 = ½m 2 v 2 /m = p 2 /2m
    • APPLICATION – ELECTRON MICROSCOPES
      • And so the momentum can be determined by:
      • P =
      • =
      • P = 1.32 x 10 -22 kgms -1
    • APPLICATION – ELECTRON MICROSCOPES
      •  = h / p = 6.63 x 10 -34 /1.32 x 10 -22 =
      •  = 5.01 x 10 -12 m
      • This value is about 100 000 times smaller than visible light.
      • 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.
    • APPLICATION – ELECTRON MICROSCOPES
      • In a Transmission Electron Microscope (TEM), the electron gun replaces the lamp and electrostatic lenses (usually magnetic lenses) replace the optical lens.
      • The electron image is converted to visible light on a fluorescent screen. The electrostatic lens is shown below:
    • APPLICATION – ELECTRON MICROSCOPES
    • APPLICATION – ELECTRON MICROSCOPES
      • 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.
      • 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.
    • APPLICATION – ELECTRON MICROSCOPES
      • A magnetic lens is shown below:
    • APPLICATION – ELECTRON MICROSCOPES
      • The result of using this lens is the same as the electrostatic lens but the path of the electrons is a little more complicated.
      • At any instant, the motion of the electron can be resolved into components parallel and perpendicular to the field.
    • APPLICATION – ELECTRON MICROSCOPES
      • 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.
      • In present day electron microscopes, magnetic lenses have virtually replaced electrostatic lenses.
    • APPLICATION – ELECTRON MICROSCOPES
      • To recap… electron microscopes can focus on smaller objects due to the fact that an electron has a smaller wavelength than visible light.
      • The electron can also be focused using electric and magnetic fields.
      • We use the ability of an electron (particle) to behave like a wave in the use this technology.
    • APPLICATION – ELECTRON MICROSCOPES
      • Scanning Electron Microscope
    • APPLICATION – ELECTRON MICROSCOPES
      • Hard Disc
    • APPLICATION – ELECTRON MICROSCOPES
      • Ant holding a microchip
    • APPLICATION – ELECTRON MICROSCOPES
      • DNA