# Wave Particle Duality .

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Wave Molecule Duality. Quantum Material science Lesson 3. Today's Targets. Clarify what is implied by wave-molecule duality. Depict the primary purposes of de Broglie's speculation that matter particles additionally have a wave-like nature. State and utilize the mathematical statement ? = h/p = h/mv
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﻿Wave Particle Duality Quantum Physics Lesson 3

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Today\'s Objectives Explain what is implied by wave-molecule duality. Depict the principle purposes of de Broglie\'s theory that matter particles likewise have a wave-like nature. State and utilize the condition λ = h/p = h/mv Describe prove for de Broglie\'s speculation.

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Wave molecule duality We have seen… … .. Photons : Quanta (particles) of light Electrons: Being diffracted. A property of waves

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Prince Louis de Broglie 1892-1987 Electrons ought not be viewed as just as particles, but rather that recurrence must be relegated to them too. (1929, Nobel Prize Speech)

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De Broglie (1924) Suggested that particles, for example, electrons may demonstrate wave properties. He summised that the de Broglie wavelength , λ was given by: m = mass v = speed of the molecule

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Note that:- This is a matter wave condition not electromagnetic wave The de Broglie wavelength can be modified by changing the speed of the molecule.

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In words...

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The diffraction tube

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Summary of Experiment Beam of electrons coordinated at a thin metal thwart. Lines of iotas cause the electron bar to be diffracted in specific headings as it were. We watch rings because of electrons being diffracted by a similar sum from grains of various introductions, at a similar point to the occurrence shaft.

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What we ought to see

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Electron diffraction 1927: Davisson & Gerner affirmed this expectation with trials utilizing electron bars. They really utilized a nickel focus rather than a carbon one (we utilized) The wavelength they gauged concurred with de Broglie There is a connection between the quickening voltage V and the k.e . of the particles

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Diffraction impacts have been appeared for Hydrogen iotas Helium molecules Neutrons Neutron diffraction is a phenomenal method for contemplating gem structures.

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De Broglie Wavelength In 1932, De Broglie found that all particles with energy have a related wavelength. What is the wavelength of an individual, expecting he/she measures 70 kg, and is running at 25 m/s?

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Practice Questions 1.Find the wavelength of an electron of mass 9.00 × 10 - 31 kg moving at 3.00 × 10 7 m s - 1 2. Discover the wavelength of a cricket bundle of mass 0.15 kg moving at 30 m s - 1 . 3. It is additionally alluring to have the capacity to ascertain the wavelength related with an electron when the quickening voltage is known. There are 3 stages in the estimation. Compute the wavelength of an electron quickened through a potential contrast of 10 kV.

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Step 1: Kinetic vitality E K = eV = 1.6 × 10 - 19 × 10000 = 1.6 × 10 - 15 J Step 2: E K = ½ mv 2 = ½m ( mv ) 2 = p 2/2m, so energy p = √2m E k = √2 × 9.1 × 10 - 31 × 1.6 × 10 - 15 = 5.4 × 10 - 23 kg m s - 1 Step 3: Wavelength λ = h/p = 6.63 × 10 - 34/5.4 × 10 - 23 = 1.2 × 10 - 11 m = 0.012 nm.

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Slit separating, d Wavelength,  Distance to screen, L Fringe dividing, x d 2 Laser d 1 L 1 Slits L 2 Screen 1 Screen 2

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End

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