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# PHYSICAL CHEMISTRY CHEM 455

UW

GPA 3.92

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This 51 page Class Notes was uploaded by Carmela Kilback on Wednesday September 9, 2015. The Class Notes belongs to CHEM 455 at University of Washington taught by Thomas Engel in Fall. Since its upload, it has received 13 views. For similar materials see /class/192532/chem-455-university-of-washington in Chemistry at University of Washington.

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Date Created: 09/09/15

H atom made up of proton and electron 2 2 mar 6 q 6 477580 r 4712901 Schr dinger equation is LEVWJ if r2 8r 8r 2 a 9 62 9 I 2 i sing 1I a 9 2 1I az 9 r st 89 89 r st 54gt 2 e IIr9 Ell7399 91 4775801 Because V depends only on r can achieve separation of variables Wr 9 Rr 9ltD 0c1gt are spherical harmonic functions Only function not known is 120 h2dr2dRrh21l1 e2 RFZERF 2urZE dr Zurz 4727801 Effective potential 92 h2111 e2 1 Vcentripetal r V r 2mg r2 2 Centripetal potential differs from Coulomb potential only for l gt 0 It keeps p d f electrons away from nucleus 93 Total energy eigenvalues are negative by convention 62 quot 8713980a0n2 2179x10 18J n 2 1360eV n2 n1234 Bohr radius a0 059A Need 3 QN to describe state of H n 1 2 3 4 10 1 2 3n 1 mlOili2i3il 32 ra0 n21l0 R10r2i e Radlal 6 0 functions 1 1 32 n2l0 R20r 2Ler2ao 8 a0 a0 Complete normalized total energy eigenfunctions include spherical harmonics nleanyzO nLlQny0 n2JLnyO n2JLnyi1 32 1 1 ra0 11000 Z a e 0 1 1 32 F r2a 2 0 W TM 1 1 32 F quot a Illzio 79995 Z m a e a 0 C089 0 0 32 1 1 r r2a iiq n9 e Oane 11211 8 77 a0 a0 Note that EF real only if m l 0 96 Convenient to combine orbital functions with their complex conjugate to create real functions 32 1 1 r r a0 wszr9 ma Oj 61 06 Sin6cos 1711Yll 32 wzpyre 1 i ie r2 sin6sin YE YE 1287 a0 a0 32 1 1 r a 11sz HEMP ma j aLe 0 c056 Ylo 0 0 97 Absorption spectrum of H M84 1 1 853W Knizniiial quotjinglj V lEiniiial E nal V h i i r1453 20000 Paschen n 2 quotinitial 1 Lyman 40000 Baimer 1 lemma 2 2 Balmer 60000 lemma 2 3 Paschen 430000 400000 11 7120000 Lyman Depicting H atom 1s total energy EF Evaluate 39Pxyz 0 2 71 Q xao xao 3D plot Contour plot 99 Leading edge of contour plot for s functions is Rr 2D ZS 33 12 To display H total energy EF other than ns need contour plot of l1quotxyz with xoryorz0 Note different appearance of angular and radial nodes W2py Vpr Calculating the probability of finding the e39 in H within d V H13 Total energy EF have nZl radial and Z angular nodes Example Problem 93 Locate the nodal surfaces in 1 2 2 1 3 r r2 W310 9 Ei2l 0 0 0 The angular part cosG is zero for 92752 In 3D space this corresponds to the plane 2 0 917 I The radial part of the equations is zero for nite values of a 0 2 Iquot Iquot for 6a 0 This occurs at r O and 0 0 at r 6 a0 The rst value is a point in three dimensional space and the second is a spherical surface 918 In atom probability of nding e39 at certain distance from nucleus of more interest than nding it in d V W at 3943 W at r for all 94 919 De ne radial probability distribution function Prdr Prdr 02 d j0 sine d6 Rr2 dr 472 r2 Rr2 dr rpd gives the probability of nding the electron in a spherical shell of radius r and thickness dr 920 rpd example for Is orbital Note that rpd function goes to zero as r goes to zero 415142 aarx a 4mg gn39Erfa i I PJ 1 422 ff 921 Radial Distribution Function is 2p 23 3d 3p 35 iHii quot 5 10 15 20 Distance a0 Example Problem 96 Calculate the maxima in the radial probability distribution for the 25 orbital What is the most probable distance from the nucleus for an electron in this orbital Are there subsidiary rnaXirna 3 2 m 47rr2R2 r r2 2 Plot Pr and dP 1 dr at3 0 ra0 8a 16a021 8a01 2 r3e VS rczz0 923 1 3 4 5 rao Principal maximum in Pr is at 524a0 Subsidiary maximum is at 076a0 Key equation in spectroscopy is hV IE2 Ell Spectral M nm v 1014 Wave Energy Spectroscopy Range Hz number kJmol cm39l Radio 1X109 10396 001 1x10394 NMR Micro gt100000 lt 10392 lt 30 lt 01 Rotational wave Infrared gt1000 lt 30 lt 10000 lt 120 Vibrational Visible 700 4 13000 160 Electronic red Visible 450 6 20000 250 Electronic blue Ultra lt300 gt 10 gt30000 gt 400 Electronic Violet 81 Energy transfer is between EM eld and molecule E F3939397 lj m k Mm 82 Basic concepts in spectroscopy 1 Wave number V Z I generally used to describe transition units cm39l Selection rules restrict possible transitions Molecule must have permanent or dynamic dipole to couple to EM eld in dipole description Raman spectroscopy can be used if no permanent or dynamic dipole 83 3 possible processes absorption spontaneous emission and stimulated emission Stimulated S ontaneous Absorption iigmission Emissmn EMMW N1 NZ atoms in lower upper state Energy At equilibrium 1312 pvN1 13211N2 14le2 16 2h 3 Bl2 BZI 321 C 8394 Vibrational spectroscopy transitions Transition probability zero unless transition dipole moment not zero At 300K usually only n0 state occupied m 1wxyxxwnxdr i o H5X HO 3n5 linear or 3n6 nonlinear Vibrational modes Anil n0 11 l dominant transition Morse potentials is realistic potential that allows dissociation Different level spacings don t I give rise to Vx multiple peaks I because only no gt O O Anharrnonicity allows An i2 i3 very weak AE between adjacent levels not all same 86 Adsorption of IR light excites normal modes not individual bonds symmetric antisymmetric stretch stretch 3657 cm391 3756 cm391 Neither mode is simple OH bond stretch because all three atoms coupled through bonds 87 IR absorption spectroscopy BeerLambert law 61711 81M 16171 11 I o 1 6 81Ml Characteristic group frequencies Group Frequency Group Frequency cm39l cm1 OH stretch 3400 CO stretch 1700 N H stretch 3 3 5 0 CC stretch 165 0 CH stretch 2900 CC stretch 1200 CH bend 1400 CCl stretch 700 88 Absorbance Experimental setup and spectra light source L 3n 69f0r g E gg CH4and 11 3n51f0r E i 1 CO Whyis number of CH4 Observed peaks different A mop 1000 1500 2000 2500 3000 3500 17 cm1 89 Rotational spectroscopy selection rule for diatomic molecules is A d 1 Permanent dipole needed to couple molecular rotations to EM eld De ne h B 87z2u r02 l 60 r trait t Energy levels given by iiZ IZZ E JJ1 JJ1hBJJ1 M lt gt WW5 lt gt ltgt AE for transitions starting at J given by AE Emea EJmma for AJ 1 h2 h2 AE 1112 JJ12hBJ1 2W02lt gtlt gt M lt gt ltgtgt andfor AJ 1 h2 h2 AE J 1J 2JJ1 2hBJ 21102 2ur0 811 Unlike Vibrational spectroscopy energy difference between adjacent energy levels not the same J16 272 hB 24OIWB ZthB 182hB 156hB 132hB lthB 72hB 42hB 20hB 6hB Because rotational levels more closely spaced than Vibrational levels Vibrational excitation will also lead to rotational excitation 813 Rotational Vibrational spectroscopy n1 J10 n1 J5 Peak frequencies equally spaced determined by energy level spacing n0 J10 n0 J5 Peak intensities determined by number of molecules of 2800 2900 3000 3100 originating level Frequency cm1 814 Intensity nJ ampe 8J80VkT 2J 1e h2JJ121kT J value of highest intensity depends sensitively on T Reconsider IR spectra for CO and CH4 815 Absorbance Un39rts 0020 0015 0010 0005 I 20 50 l 2100 I 2150 Wavenurrber cm l 816 Particle in nite depth box more realistic model for confinement Potential de ned by V 39 Vx La2 gtx gtra2 VxVnx22ZxsraZ nzixaaz oxxdifferent inside and outside box Inside box d W X 7 ix m 2 WM Outside box dZV l LZWU E or a LyxAe Bequot foreaszgand LyxA e B equot formsxsg Characteristics ofEF of Inside box similar to infinite box Add 12 mvelength as increase n Outside box 39 Boundary conditions make B A 0 Finite number of bound states 2 0 wxdecays most rapidly for energy eigenvalues near bottom ofbox Decay of LAX outside box Note dependence on n 2mVan h 7 u u mmxum Model atoms e in molecule 1 l by finite depth box Only valence electrons overlap allowing bond fonnatiom Model nnetwork in PIB model 6 7r electrons a c a new w 45m BWAE m a agzpm Excited state populated at 298K AE given by 2 h n in 7x6626x10 15 AE 2 2 3m 8x911 x10 3 kgx973x10quot2m 445x10quot91 a 445x in n X X 47 A e 7 2 122 inxm KEIEIK Zilxlo g Classical physics can t explain electrical conduction Periodic array of Na atoms is 1D Wire x Looks like l l l PIB for Wlence electrons Metal in PIB model t r W MMIlVl m m Insulator in PIB model For insulator band completely lled 7 nmmmmm 7 H7 nAInAnnnnnnm 7 nmnmmmm Tunneling through barriers Particles go through as well as aver barriers Gerd Bihhag hghc and Heinrich Rohrer 1m S tunneling microscope Principle behind microscope Exponential dependmce OH on distance gives high Spam resolution Electrolytically etched tips can have radius of 20 nm Most STM studies require ultrahigh Vacuum Titanium dioxide surface Silicon Single Crystal Surface Filled 1m and empty ght states ofSi111 7x7 can be imaged The helm pitch m DNA can be agged anecuy An electxun canal s farmed by 48 Fe atums Bu a cuppa surface V I MINDyrquot Stages m cunmcung the ma Electrical conduction through molecules Use Atomic Force Microscope for this expt 0 quot 105 DlSIanCE quotml iauelleaJ manuals numaa Tunneling ofC in chemical reactions 39 Band structure ufGaAs and Al duped GaAs Me A Gm Curmnzmu Band stxuecure ufhetaumcture Me As cwmmw ME As em gap um um Quantum Dots Energy levels depend un sue e am etherefurelxght absurbeduramttedalsu depends un sue Intemal Illumination ofLiving Organisms sing Quantum Dots

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