CH7_quant_notes.W9

CH7_quant_notes.W9 - QUANTUM MECHANICS ' Cha‘ter7...

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Unformatted text preview: QUANTUM MECHANICS ' Cha‘ter7 Electromagnetic Radiation FIG I - Electromagnetic Radiation Amplitude] . wave properties Direction of propagation FIG II - Electromagnetic Spectrum 7 EXl. What is the frequency of 520 nm green light? Wavelength (nm) _>. 10—2 100 102 104 106 103 1010 1012 I I my : X-ray lviolet v inflamed Microwave : Radio frequency I z ‘ | I g I "—r-T—‘W—i—‘F‘T . —l_"T"-T—i_|—l—l_ 102.0 1018 1o16 1014 mi“ 1010 10B 106 104 ' <— Frequency (5“) 400 500 600 750 nm Visible region 7.5x1ol4 6.0x1014 5.0x1014 4.o><1o14 5-1 FIG III - Diffraction Direction of Trajectory light wave of a pebble particle properties refraction Crests of . Beam of , particles _2_ Problems that Classical Physics Could Not Explain 0 blackbody radiation FIG IV - Blackbody Radiation: Light (Planck quantized vibrational energy) Emitted by a Heated Object Frequency, v (TI-12)» 1500 750 500 3 5 300 250 214 187 167 150 136 l | I I ,____, I l What is the energy of a mole of 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 . ' Wavelength, 2. (nm) nm photons? - photoelectric effect FIG V - Photoelectric Effect (Einstein quantized light) ~ Iv<vo vzv0 Kinetic energy = % me»2 Metal 0 Frequency, v I Maxlmum klnetlc energy, 5 119.502 I =- a" meu2= h(v— v0) = by — hv‘1 (b) EX 3. The longest wavelength of light which can ionize metallic cesium is 600 nm. What is the binding energy of these electrons? ° stability of atoms and emission spectra (Bohr quantized matter) FIG VI - Emission Spectrum of FIG VII - Emission Spectra of Some Hydrogen '- Elements Gas discharge tube contains hydrogen Mnm) 400 500 600 700 "9 Ne Bohr Model of Hydrogenic Atoms FIG VIII - Energy Levels of Hydrogen Atom 5.45 x 10-91 a -§Ry *AE‘. -(er 5;) ‘ In) = th‘A V l l - an “at ...___3 ’ ‘3‘ J “6‘ we '7,“ = KYDBEI'LG : 09 s -r ‘ 3' 2 ‘3 _L. .L.) ~ I) W i “‘3‘ “‘3‘ “it 0".‘I “$§1) u. 22R 1 E, = —2.18 x 104313:ka | y - - n I L man Balmer liaise-he; Bracket! Pfu d .- E = — R 18 R dber constant in] y .._.._....,... “I " n2 ( y y g ) UN , via beatnik 12 2 1 1 —AE = -(Ef—E,-) = hv = Z Ry "—2—? f i Effnfiiééfi ' Visible \ ——100 WWW ——200 U I ('71 = 1) Ilravlo et — —21 8 - - 1 B Wavelength (nm) Energy x 1020 (Jlalom) ATOMIC ORBITALS Quantum mechanical view of the atom Background Bohr — old quantum theory (E exact) wave—particle duality de Broglie — matter waves: mul : h Description of State of the System Heisenberg, Dirac (very abstract) Schrodinger equation: F1 1/1 = E 1/1 1/1 is the solution Heisenberg uncertainty principle: A(mu)Ax 2 11/47: Wavefunction w Born - It/Il2 is probability density rzll/Il2 - radial probability distribution y/(x, y, z) is an orbital quantum numbers: n, 1, ml (also ms) 112 orbitals l=0——>s,l=l—>p,l=2—>d, l = 3 —> f, g, - ~- n— 1 nodes => l//=0 n — l — 1 radial (spherical) l angular A Musical Analogy for Nodes ‘ FIG IX - Standing Waves for a String Quantum Numbers (and nodology) l — angular momentum m l - magnetic FIG X - Nodes for a Vibrating String ’ E 1half—wavelength E n=2 L=2(—;”-) 2 half-wavelengths -5- Shapes of Atomic Orbitals: Radial and Angular Nodes importance FIG XI - 2D Radial (Spherical) Nodes FIG XII - s Orbital Radial Nodes (l = 0, m, = 0) => 1 orbital FIG XIV - p Orbital Angular Nodes (l = 1, ml = -—1,0,— 1 => 3 orbitals) 2px z FIG. XV - d orbitals ‘ (1 _=2, ml :5 52,:120, 1, 2 => 5 orbitals) determines the chemistry of transition ele- ments and their coordination compounds «1,, . Z l (I!) Where is the Electron? FIG XVI - Radial Probability Distribution M mini. Vuenuuw a- w "5} ‘ Mame» 03' i ‘ m r n u.5 L!) L: 2n 2.: 3.0 3.5 0 arm L6 2‘0 2.5 an n o ILS I.- u 2.0 u so u . .. o M. . .. M .5 0.05 M. 04 um owl R. 04 R.‘ 0.: HR.‘ V as m; 02 mm! “' nos -n.z 0" ' r o 2.0 4.0 0.0 5.0 o 2.0 to 3.0 no u 0.1“ 1.0 me u 040 ’/" 0.15 'l“ ""‘ 0.30 now M“ as 3. ON ' ,3.- nm “Jam ’ Mo 1 ‘ 0-005 um - .om , ‘ a A one «no _ o 2.0 1.0 «.0 w n 10 m mo no no 0 2.0 an mo 14.0 m: 7/3: ’1‘ 'l. a o I 9 0025‘ n- E“: -__.g n‘ ‘I 3 at Mount. 0006: = 1. 1 V than“) ' . (r) a .%3 0.“ °- . 1 0.10 . a R. h' ,1..- P a“ I no] I - P o 1.02.08.04.0'53101010'3 o u to m to . o m zomwwmuun _ "fl . _ 7/. 7". 0.12 V non _ . ml a V n.‘ or“ I r'R.- V no: om: 02‘1ll0flfll‘ll ozcllloulnon n aclllluunu- . rid. . r/I- VIO- _ M mum at ' on . . “‘ mam ' an: oz4¢oionuun oadclmlauxois ozqalmnuww m. m, Wu). uth I .ratl‘ftrw” ‘ ‘ (Punt) - (Datum) ...
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This note was uploaded on 04/13/2010 for the course CHEM 114 taught by Professor Jursich during the Spring '08 term at Ill. Chicago.

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CH7_quant_notes.W9 - QUANTUM MECHANICS ' Cha‘ter7...

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