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Dual Nature of Matter Wave-Particle Duality of Matter

Dual Nature of Matter Wave-Particle Duality of Matter. Louis de Broglie (1923) postulated the wave-particle duality of matter:. P = m v = h . m v = linear momentum. = de Broglie Wavelength de Broglie postulated that particles exhibit a wave-like nature with a

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Dual Nature of Matter Wave-Particle Duality of Matter

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  1. Dual Nature of MatterWave-Particle Duality of Matter • Louis de Broglie (1923) postulated the wave-particle duality of matter: P = m v = h  m v = linear momentum • = de Broglie Wavelength de Broglie postulated that particles exhibit a wave-like nature with a wavelength related to the particle mass and its velocity, or to its linear momentum. As the mass increases, the wavelength decreases and therefore becomes less important and does not exhibit itself. See the example calculation that follows.

  2. de Broglie wavelength and particle mass • Electron me = 9.1110-31 Kg, v = 1.0  107 m/s • Ball mball = 0.10 Kg; v = 35 m/s Is there experimental evidence to support this postulate?..YES…

  3. Testing de Broglie relationship Davisson and Germer—diffraction of electrons 1927 Constructive and Destructive Interference of Waves X-rays shining on a crystal give interference pattern (diffraction pattern). Using electrons (accelerated to 107 m/s) with the same de-broglie wavelength as X-rays. Ǻ length scale = spacing between atoms.

  4. Diffractions Patterns:Electrons with wave-like characteristics Yes it is TRUE (1929-de Broglie awarded Nobel prize)

  5. Introduction to the Atom • Thomson Discovery of the Electron • Rutherford Discovery of the Nucleus First idea of the atom was proposed by Greek philosophers Democritus and Leucippus about 400 B.C. It was intuition. First experimental evidence by Lavoisier on Chemical Reactions

  6. Thomson Discovery of the Electron 1898-1903 When a high voltage was applied between the electrodes in a partially evacuated tube, a ray was produced, from the cathode to the anode. It was repelled by the negative pole of an electrical field. It deflected in a magnetic field. The electrons excite the gas in the tube which causes a glow. The green color is due to a screen coated with zinc sulfide. e/m = -1.76  108 C/g Plum Pudding Model Millikan Experiment: me = 9.11  10-31 Kg

  7. Rutherford Discovery of the Nucleus(1911)atomic model: the nuclear atom 7300 time more massive than the e +2 charge (He2+)

  8. PROBLEM: Explaining the enormous stability of the atom

  9. BY CLASSICAL PHYSICS: The ATOM IS UNSTABLE • The electron was thought to orbit the nucleus like planets around the sun. • A charged particle can be made to travel in a circle by application of a force towards the circle center. • An electron changing direction constantly is under acceleration. • According to classical physics, a charged particle under acceleration should constantly emit radiation, and should therefore eventually fall into the nucleus! In Classical Terms, the Atom is UNSTABLE

  10. BOHR (1913)through the application of quantum hypothesisgave an explanation to the atom unusual stabilitythe atom can change its energy only by discrete quanta. Therefore there are only discrete stationary states the lowest of which is the ground state. After any interaction, the atom goes back to ground state. This explained the line emission spectrum of the hydrogen atom

  11. Line Spectrum vs. Continuous Spectrum Continuous Spectrum Line Spectrum

  12. Violet, Blue, Green, Orange at 410 nm, 434 nm, 486 nm, 656 nm

  13. The Bohr Model for H-Atom Niels Henrik David Bohr (1885-1962) Bohr Postulates that the electron angular momentum is quantized: mvr = nh/2 n = 1,2,3,… (integer or quantum number) The electron orbits the nucleus in specific orbits of specific radii, and has specific (quantized) energies

  14. The Bohr Model for the H-atom Bohr balanced the coulombic force of attraction (e2/4πεor2) and the centrifugal force (mv2/r) Allowed the angular momentum mvr to take on only specific values = nh/2, where n is an integer Doing the math yields an equation for allowed radii for the electron orbits and for the allowed energies of the electron as a function of n Derivation will be posted on Moodle and discussed in recitation- try it at home

  15. =

  16. The Bohr Model The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits with specific radii (see posted derivation on Moocld). • E = energy of the level n for H and H-like (ions that have a nuclear charge z and 1 electron left, such as Li2+ (z=3), Be3+ (z=4) • z = nuclear charge (for H, z = 1) • n = an integer (1, 2, 3, 4, ….) Rydberg constant H-like ions: ex. Z=3 for Li2+: H-Atom:

  17. Specific Orbit Radii Quantization of Energy r=aB=0.529 Å (Bohr radius) Bohr Frequency Condition: n = 1 is ground state (most negative energy) n> 1 is an excited state

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