Lecture3(Quantum Chem) Ks

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  • K. SumithraCHEMISTRY I (CHEM C141)Lecture 3: 9/8/2010

  • SUMMARY OF THE LAST LECTURE

    Black Body Radiation - featuresPlancks Distributions:Concept of QuantizationPhotoelectric Effect: Ek = h = h( 0)Particle nature of light

    Line Spectra: E = E2 E1 = hConvincing evidence for Quantization

    Bohr Atom Model

  • Atomic and Molecular SpectraThe energy of the atoms or molecules is confined to discrete values, so energy can be discarded only in packets.A region of spectrum of radiationemitted by exited iron atoms Spectrum due to sulphur dioxidemolecules

  • Bohr model of hydrogen-like atom

    To account for the line spectrum, Bohr proposed stable orbits (or energy levels), for the electron, given by the quantization condition for angular momentum mvr = nh/2 = n, n = 1,2,3,.

  • Bohr Model 1. Specific orbits, discrete quantized energies. 2. The electrons do not continuously lose energy, but gain or lose by jumping from one orbit to another 3. quantization of angular momentum L = mvr = nh/2 = n, n = 1,2,3,.Success Could explain Rydbergs formulaTheoretical background for Line Spectra

  • Bohr model InadequaciesPrimitive ModelSemi-classicalThe spectra of larger atoms. The relative intensities of spectral lines.The existence of fine and hyperfine structure in spectral lines. The Zeeman effect - changes in spectral lines due to external magnetic fields.

  • Waves and ParticlesMain experiment showing light as particles are thePhotoelectric effectBlack body radiationTwo properties of waves are:InterferenceDiffractionIf electron is acting as a wave, We should see diffraction and interference of matter waves

  • Wave-Particle DualityDouble-slit ExperimentInterference: Superposition of two or more waves to generate new patternsConstructive; destructiveWave-Particle duality shows:Light can act like a particle.Particles can act as waves

  • The wavefronts resulting from two slits.Youngs double-slit experiment can be done with electronsElectron behaving as a wave!

  • Two waves in phaseTwo waves 180 out of phasecombined waveformwave 1wave 2constructivedestructiveInterference

  • Electron DiffractionFiring electron at an object and observing the scattering (analogous: X-ray and neutron diffraction): Davisson and Germer 1925investigation of the angular distribution of electrons scattered from nickel. :electron beam was scattered by the surface atoms at the exact angles predicted for the diffraction of waves, with a typical wavelength

  • Braggs lawn=2d sin()- wavelength of the electron waveA pattern of sharp reflected beams from the crystal

  • DualityGirl friend or her Granny?

  • wave-particle dualityThe ability for something to behave as a wave and a particle at the same time is known as wave-particle duality.

  • It combines two contradictory features or qualitiesThat does not mean that it is false! It is a fundamental property of the universe.Duality is a paradox

  • Matter-Wave DualityOrthodox Quantum physicist : Duality is a phenomenon that can be viewed in one way or in another, but not both simultaneously.Second-order consequence of various limitations of the observerWaveparticle duality is deeply embedded into the foundations of quantum mechanics

  • It is difficult to draw a line separating waveparticle duality from the rest of quantum mechanics.In electron microscopy where the small wavelengths associated with the electron can be used to view objects much smaller than what is visible using visible light.Applications of Duality2. Neutron Diffraction uses neutrons with a wavelength of about 1 , the typical spacing of atoms in a solid, to determine the structure of solids.

  • Evidence for wave-particle dualityElectron diffraction Interference of matter-waves Photoelectric effect Compton effect There are therefore now two theories of light, both indispensable, and without any logical connection.Einstein, 1924Evidence for wave-nature of matter, lightEvidence for particle-nature of light

  • Light comes in discrete units (photons) with particle properties (energy and momentum) that are related to thewave-like properties of frequency and wavelength.MATTER WAVESPrince Louis de Broglie 1923Postulate : Ordinary matter can have wave-like properties, with the wavelength related to momentum p.

  • Wave-Particle Dualityp = h/A particle moving with linear momentum p, has an associated matter-wave of wave length: = h/pMatter wavesde Broglie:

  • = h/p

  • Calculate the wavelength of an electron in a 10-MeV particle accelerator. (1 MeV = 106 eV) Solution: We need to find the momentum, p, from the energy, E. The relationship between them is p = (2mE)

    P = (2 x 9.11 x 10-31 kg x10 x106 x 1.602 x 10-19 kg m2 s-2) = 1.7 x 10-21 kg m s-1= h/p = (6.626 x 10-34 J s)/(1.7 x 10-21 kg m s-1) = 3.9 x 10-13 m = 0.39 pm

  • C60 fullerenes wave manifestation: Large, massive object (diameter is in nanometer range)de Broglie wavelength is 2.5 pm i.e. about 400 times smaller than diameter. Journal: Nature 401: 680-682, 1999 Largest object for which quantum-mechanical wave-like properties have been directly observed in diffraction. BuckminsterfullereneBucky ballUniversity of Vienna, Austria.

  • Are there waves associated with macroscopic objects?Wavelengths are immeasurably small

  • A human being weighing 70 kg, and moving with a speed of 25 m/s ~ 3.79 x 10-37 meters. A ball weighing 100 g, and moving with a speed of 25 m/s ~ 2.65 x 10-34 meters. An electron accelerated through a potential difference of 50 V ~ 1.73 x 10-10 meters. Some Typical de Broglie wavelengths

  • Uncertainty Principle No physical phenomena can be described by only classic point particle or wave Neither the wave or particle description is fully and exclusively accurateDuality ; Consequence

  • A property of Conjugate variables : share an uncertainty relationTime and FrequencyPosition and Momentum

    Uncertainty

  • Heisenbergs Uncertainty PrincipleIt is impossible to specify simultaneously, with arbitrary precision, (a given Cartesian component of) the momentum and position of a particle.px x /2

    Complementary variables, increase in the precision of one possible only at the cost of a loss of precision in the other. x- uncertainty in position

    p- uncertainty in momentummv.x h/4 =h/2

  • Uncertainty PrincipleDefinite wavelength Definite momentum but since wave is spread out everywhere, no information about position.

  • Hard to understand duality, matter waves, uncertainty?

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