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# Physical Chemisty II CHEM 4310

WMU

GPA 3.81

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This 15 page Class Notes was uploaded by Corbin Crist DDS on Wednesday September 30, 2015. The Class Notes belongs to CHEM 4310 at Western Michigan University taught by Yirong Mo in Fall. Since its upload, it has received 36 views. For similar materials see /class/216963/chem-4310-western-michigan-university in Chemistry at Western Michigan University.

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Date Created: 09/30/15

Classical Mechanics Classical physics Newton s laws of motion for particles 0 Precisely predict the locations and momenta of particles at each instance The translational rotational and vibrational modes of motion can be excited to any energy The electromagnetic spectrum Wavelengthm 1 10 1 10 2 10 3 10 1 10 1o 10 7 10 10 9 104 10 1oquot2 10 10quot E E E E c E E E 1 E E E a c a v Q o Radio ICFO E m Vacuym ra ra osmlc wave mffared E ultravtolet y V y rays 5 Molecular Molecular Electronic Coreelectron Nuclear rotation vibration excitation excitation excitation Classical Mechanics Failures of classical mechanics Observation of black body radiation Heat capacities for a monotonic solid Atomic and molecular spectra Compton scattering Photoelectric effect Optical spectra Twoslit experiment BlackBody Radiation Detected radiation Pinhole Container at a temperature T Fig 1 Radiation from a black body Enevgy distribution p Fig 2 cavity HOW to explain the experimental results Maximum Increasing temperature Wavelength A Energy distribution in a black body BlackBody Radiation Classical physics Rayleigh Planck s theory The electromagnetic field is a collection The energy of each electromagnetic of oscillators of all possible v oscillator is discrete quantization of energy Enhv 110 12 87rkT 25 Rayleigh p 4 7 A 5332 L l 20 c 5 quotA 7 g 15 Experimental f Pianck 5 distribution E E 10 5 0 05 10 15 20 Wavelength A IlkThc Fig 3 Ultraviolet catastrophe Fig 4 The Planck distribution Heat Capacity Dulong Petit law The molar heat capacities of all monoatomic solids are 25 J K 1 mol39l CVM 2 3R Experiments CV90WhenT0 Einstein s theory Each atom oscillates With a single v and the oscillation energy is nhv o 05 1 15 2 TaE Fig 5 Einstein s curve ts the experimental data Atomic and Molecular Spectra Emission intensity 415 Wavelength lnm Fig 6 Emission spectra by excited iron atoms Absorption intensity Anm Fig 7 Absorption spectra of S02 E3 hvEJ EZ gt E E 2 hv Er E m JVV hu E3 E gt W Fig 8 Interpretation of spectroscopic transitions WaveParticle Duality The particle character of electromagnetic radiation Q1 Calculate the number of Photoelectric effect photos emitted by a 100 W yellow lamp in 10 s Take the wavelength of yellow light as 560 nm and assume 100 efficiency colleetorplate 1 mev2 h V q 2 no current ows Electron diffraction Evidence for the wavelike character of electrons Electron Nickel crystal WaveParticle Duality The duality of light 2 h Emc hv 1723102 All particles have the duality l h l 7 de Broglie relationship 7 HIV E is a 39 1 2 h I Ez mv2Vp V gt it 2 2 quot J 2mE V Q2 What is the de Broglie wavelength of an electron that has been accelerated through a potential difference of 100V E 8V 1602X1019C100V 1602gtlt10 19 J 6626X1034 J s5403gtlt124 kg m 5 1 1226gtlt1010 m A h VZmE The Solvay Congress of 1927 Dirac De Broglie Schr dinger Heisenberg The Schriidinger Equation Classical timeindependent wave equation d2wx 212 dxz Jvx 62 62 62 2 2 Wxayaz7 j WOQJCZ 6x2 6y2 622 For quantum mechanical particle h 12mE V 7 12 02 02 02 V E 2m 0x2 3y2 azzjll V V I TimeIndependent Schriidinger Equation J Wavefunction 1 Interpretation of the wave function by Born dx 39 PrTngilitv Probability density w vfxIx 1 X IA xxdx LO V xvxdx 1 Interpretation in 3D space dZ39 dxdydz r2 sin 6drd6d The wavefunction contains all dynamical information about the system it describes A wellbehaved wave function should be 0 Finite Singlevalued Continuous and have a continuous slope Normalized Wavefunction 1 Which of the following wavefunction is acceptable and Why V a c Wavefunction 1 For a particle moves along the x axis Without potential energy 2 2 2 2 h d 2VEV gt yerih Be and Ezk h 2m dx 2m lull 1 Assume A or B 0 lm em sin kx W2 A2 0r lwlz 32 Assume A B Iy2 4Azcos2 kx node Operators Operator mathematical operation that is applied to a function Linear operator AdamMM Acf cAf Hamiltonian operator if A VZ Vx y 2vx y Z H U106 y Z E U106 y 2 Eigenfunction and eigenvalues A Eigenfunctions corresponding to different A ln an ln eigenvalues of the same operator are orthogonal 00 0 fori7 j menwxow6y 1 forij Question What are the eigenfunctions and eigenvalues of the operator ddX Is 6 an eigenfunction of ddX Operators Each classical observable is associated with a quantum mechanical operator Converting a function in a classical mechanics to a operator in quantum mechanics A A 6 q q pq lh 6q Hamiltonian function 2 2 2 PX Py P2 V HEV 2m Hamiltonian operator A 2 H V2 V 2m Commutative operators l z i Question What is communicator of 3 and 13x

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