Wave Nature of Matter

Transcription

1 Wave Nature of Matter

2 Wave-Particle Duality de Broglie proposed that particles with momentum could have an associated wavelength (converse of photons having momentum)

3 de Broglie wavelength h λ = p or p = h λ only small, high speed particles will show wave characteristics (diffraction, interference)

4 normal sized objects have wavelengths that are too small to be noticed, but for elementary particles, the wavelengths are the size of nuclei

5 Example A 0.15 kg baseball is moving at 40 m/s. Determine its de Broglie wavelength

6 Solution λ = h p J s λ = 0.15kg 40m/ s λ = m Atomic diameter: m Nuclear diameter: m

7 Example An electron is accelerated from rest by a potential difference of 1.50 kv. Determine the de Broglie wavelength of the electron.

8 Solution

9 Evidence Davisson and Germer reflected a beam of electrons off a crystal and obtained a series of maxima and minima patterns (just like a beam of light would give a series of light and dark bands when it passed through a diffraction grating)

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11 Thomson G.P. Thomson detected electron diffraction patterns by passing a beam of electrons through a metal foil and obtaining an interference pattern

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13 X-ray beam through Al foil Electron beam through Al foil

14 The Nobel Prize in Physics 1937 was awarded jointly to Davisson and Thomson "for their experimental discovery of the diffraction of electrons by crystals"

15 Significance of the de Broglie Hypothesis extended Einstein's work to relate the observed wavelength of matter to its momentum showed that wave particle duality was not only a strange behavior of light, but was a fundamental principle exhibited by both radiation and matter.

16 Back to Bohr de Broglie s theory of matter waves can be used to explain why electrons did not radiate in the Bohr model de Broglie viewed the electron as a standing wave the wavelength would be longer in higher energy levels because the electron speed is lower

17 the circumference of an allowed orbit would be a whole number of electron wavelengths

18 if a whole-number of wave lengths don t fit the circumference, the result is destructive interference

19 Classical view of electrons (electrons are particles) Lots of electrons pass through top opening Lots of electrons pass through bottom opening No electrons land directly on centre of screen

20 Electron diffraction When electrons are fired through 2 slits, a diffraction pattern forms whether electrons are fired one-by-one or in a continuous stream

21 Single electron events built up from an interference pattern in the double-slit experiment.

22 Quantum Mechanical Model Quantum mechanics combines the particle-wave nature of matter and energy into a single theory

23 according to quantum mechanics, electrons do not exist in well defined orbits as proposed by Bohr quantum mechanics refer to orbitals

24 the theory can only predict the probability of finding an electron in a certain region of space around the nucleus due to the wave nature of matter

25 Electron Cloud the region where the probability of finding an electron is high

26 Bohr s idea of allowed energy states still applies An electron will have 1 of the allowed energy states, but the state doesn t correspond to a particular orbit

27 Distance from nucleus

28 Higher energy states means a higher probability of finding the electron further from the nucleus

29 Wavefunction The wave function represents the probability of finding a given particle at a given point. These probability equations can diffract, interfere, and exhibit other wave-like properties

30 Compare and contrast: waves & Waves Extended in space particles Points Particles Continuous Obey wave equations Diffract and interfere Have amplitude, wavelength, frequency & velocity Discontinuous Obey equations of mechanics Collide and bounce Mass, size, velocity, momentum

31 STS Electron microscopes use the wave nature of electrons to produce magnifications much larger than with optical microscopes The wavelengths are about ten thousand times smaller than that of light

32 Electrons are accelerated from the electron gun to the anode. The magnetic lens exerts a force on electrons; they spiral and become focused Scanning coils deflect the beam of electrons back and forth across the specimen

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34 Detecting Gravity Waves Gravitational waves are ripples in the fabric of space and time by the collision of two black holes or by the cores of supernova explosions.

35 Detecting Gravity Waves Gravity waves will compress space in 1 direction and stretch it in the other. Light is split into two beams

36 Detecting Gravity Waves If the lengths of both arms remain unchanged, the 2 combining laser beams will cancel each other out

37 Detecting Gravity Waves If a gravity wave changed the length of the arms, the light beams would not cancel out, changing the interference pattern