Section 41: The Wave Way of Particles.


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Section 41: The Wave Way of Particles. 41-2: de Broglie Waves. Louis-Victor de Broglie (1892-1987). 1924: predicts wave nature of particles Photons have wave/molecule nature Symmetry proposes particles ought to have wave nature
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Section 41: The Wave Nature of Particles 41-2: de Broglie Waves

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Louis-Victor de Broglie (1892-1987) 1924: predicts wave nature of particles Photons have wave/molecule nature Symmetry recommends particles ought to have wave nature Corpuscular nature of photons gives us E=hf , yet f is identified with the wave way of light. The two must be personally joined.

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de Broglie Wavelength Use same relationship as characterized by Einstein: Any molecule that has energy, has a wavelength connected with it. (N.B. v is a pace, not a speed!)

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Wave Nature of Particles Photon/light – wave in electromagnetic field Matter – likelihood conveyance Average likelihood of area of molecule

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Quantum Mechanics Particles have wave nature connected with their normal likelihood of area We can’t know * BOTH * a particle’s position in space and its energy in the meantime (more to go ahead this later…) Fuzzy matter…

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Calculating de Broglie wavelength Need matter that has force: individual riding a bicycle. m = 80 kg v = 9 m/sec

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Activity There is an understudy who is pursuing a school transport. She is going as quick as she can to get the transport, and the transport is ceasing to give her a chance to make up for lost time. Given that the individual\'s mass is 70 kg, her pace is 2 m/sec, the transport\'s mass is 3,000 kg, and the transport\'s rate is 0.1 m/sec, (a) what is the de Broglie wavelength of the individual? (b) What is the de Broglie wavelength of the transport? (c)Which one is greater? (d)What ought to change if their de Broglie wavelengths are the same? Roll out the fundamental improvement! (N.B. the individual is running as quick as she can !)

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Solution m = 70 kg v = 2 m/sec m = 3,000 kg v = 0.1 m/sec

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Solution (individual)

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Solution (transport)

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Solution (examination) The person’s de Broglie wavelength is greater than the de Broglie wavelength of the transport! The more monstrous an item is, the littler its de Broglie wavelength. Since the individual is running as quick as possible, the transport must go slower to persuade their wavelengths to be the same. How quick ought to the transport be going?

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Solution (proceeded)

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de Broglie Wavelength These numbers are little! Size of iota = 10 - 10 m So, the de Broglie wavelength of an article is truly just fascinating when l de Broglie >10 - 10 m. (This is the reason transports are not “fuzzy”!)

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What might we be able to change to make the de Broglie wavelength fascinating? h is Planck’s steady (a *very* little number) v is the object\'s pace (as a rule not little) m is the object\'s mass Subatomic particles have *very* little masses!

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de Broglie wavelengths of subatomic particles If we diminish the sufficiently mass (10 - 26 kg), the de Broglie wavelength can be on the size\'s request of the molecule for a huge scope of velocities. For such particles, we ought to see them act as waves do: Electron diffraction (coming soon!)

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Implications of the wave way of particles The Bohr iota Including the wave nature in the photo of an electron makes the thought of quantized vitality levels appear to be substantially more regular. Before: Angular force is quantized (not by any stretch of the imagination instinctive – mass, speed and range are not quantized!) Now: Standing wave modes clarify why electrons exist with discrete energies inside of a particle (permitted vitality levels exist in light of the fact that a standing wave design with a whole number of wavelengths can exist at those energies)

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Minute Paper What is most clear, on account of today’s class? What is still indistinct, on account of todayâ

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