Chemistry 1B Fall 016 quatizatio of eergy Chemistry 1B Fall 016 sessios lectures 3-4 E photo = h absorptio ad emissio spectra of hydroge atom 18 Z E. 17810 J Z=1 for H atom, =1,, 3,... 18 1. 17810 J 1 1 7 1 1 1 Z 1. 0967 10 m Z hc 1 1 (537-54, *(543-549), 549-557) 1 wave-particle duality diffractio of electros- (Davisso-Germer Experimet; p. 530) De Broglie relatioship (p. 58) (HW#1 1.3,1.35) What is meaig of electro wave?? (http://phys.educ.ksu.edu/vqm/html/doubleslit/idex.html) (http://www.youtube.com/watch?v=dfpeprq7ogc) Wavelegths of ordiary objects (p. 58, example 1.) Silberberg Table 7.1 (HW#1 prob S) What to do?? ivet quatum mechaics!!! Compto Experimet Heiseberg ucertaity priciple (p. 539) boig!! (HW#1 1.49) 3 4 Solvay Coferece 197 fuel for quatum mechaicias The mid-190's saw the developmet of the quatum theory, which had a profoud effect o chemistry. May theories i sciece are first preseted at i teratioal meetigs. This photograph of well-kow scietists was take at the iteratioal Solvay Coferece i 197. Amog those preset are may whose ames are still kow today. Frot row, left to right: I. Lagmuir, M. Plack, M. Curie, H. A. Loretz, A. Eistei, P. Lagevi, C. E. Guye, C. T. R. Wilso, O. W. Richardso. Secod row, left to right: P. Debye, M. Kudse, W. L. Bragg, H. A. Kramers, P. A. M. Dirac, A. H. Compto, L. V. de Broglie, M. Bor, N. Bohr. Stadig, left to right: A. Piccard, E. Heriot, P. Ehrefest, E. Herze, T. De Doder, E. Schroediger, E. Verschaffelt, W. Pauli, W. Heiseberg, R. H. Fowler, L. Brilloui. 5 6 1
Chemistry 1B Fall 016 quatum mechaics: WEIRD Quatum Jujitsu π Quatum Mechaics 7 8 what quatum mechaics must iclude goals of lectures 3-4 particles have wave-like properties some properties, like eergy, ca oly have certai values (eergy is quatized) the emissio or absorptio of photos result i the system goig from oe state to aother the quatum mechaics of the hydroge atom (ucleus + electro) what is the quatum mechaical equatio that determies the properties of electros i atoms ad molecules? what are the allowed (statioary) states i which the electro i a hydroge atom ca exist? what will be the eergy of a electro i a give state? what are the probability waves (orbitals) that describe the where a electro i a give state will be foud? 9 10 Bohr model vs Quatum Bohr model got the eergies of allowed levels correctly However Bohr model assumed electros travelig aroud ucleus i orbits of fixed radius (differet radii for differet s) ad with specific E This is icosistet with the wave properties of electro ad Heiseberg Ucertaity Priciple Schrödiger equatio (see pp 540 ad 549) SCHRÖDINGER EQUATION H E m V E basic equatio of quatum mechaics what does it ivolve?? (chem 163A) what does it tell you?? E electro orbits: o, o where ca you lear ALL about it i electro orbitals : si, si upper divisio chemistry? (probability waves) 11 ot resposible for pp. (543-549)*, Table 1.1 1
Chemistry 1B Fall 016 hydroge s electro waves: the three quatum umbers (pp. 550-551) poit i space,, m r,, the pricipal quatum umber the agular mometum quatum umber m the magetic quatum umber Chemistry 1B AL the Hydroge Atom Allowed Quatum Numbers Table 1.1**** 13 14 study guide II, sectio III (clicker credit) Schrödiger equatio (see pp 540 ad 549) SCHRÖDINGER EQUATION H E m V E basic equatio of quatum mechaics what does it ivolve?? what does it tell you?? 15 where ca you lear ALL about it i upper divisio chemistry? ot resposible for pp. (543-549)*, Table 1.1 16 hydroge s electro waves: the three quatum umbers (pp. 550-551) hydroge s electro waves: the three quatum umbers (pp. 550-551) H E,, m wavefuctio or orbital that describes allowed states of electro poit i space,, m r,, the pricipal quatum umber the agular mometum quatum umber m the magetic quatum umber 17 18 3
Chemistry 1B Fall 016 rules for allowed quatum umbers rules for allowed quatum umbers pricipal quatum umber = 1,, 3,...., positive, o-zero, itegers agular mometum quatum umber for give value of = 0, 1,,... (-1) zero ad positive itegers < 19 0 rules for allowed quatum umbers agular mometum quatum umber desigatios of orbitals with various values of 0 1 3.. s orbital p orbital d orbital f orbital.. from spectroscopy sharp pricipal diffuse fudametal 1 HW#1 10, 11, 1 rules for allowed quatum umbers magetic quatum umber m for give value of allowed m are positive ad egative itegers from to + icludig 0 m =, +1,, 1,0,+1, +... + or m = 0, 1,, HW#1 10, 11, 1 3 4 4
Chemistry 1B Fall 016 Zumdahl Tables 1. ad 1.3 HW#1 10, 11, 1 5 6 learig objectives II (ad clickey-click) quatum mechaics of the hydroge atom (the electro waves i H atom ad their physical meaig) quatum umbers of allowed orbitals table 1. ad 1.3 eergies ad sizes of orbitals HW#1 10, 11, 1 orbitals ad the electro desity diagram orbital (wavefuctio, ) [ ca have relative sig, values] electro desity (probability, ) [ 0] radial probability distributio (4r ) Fig 1-16 & 1-17 hadout figures 7 8 CHEM 1B-AL video is fiis Wedesday, 4 October!!! iclicker Check Up exercise Study Guide I III How s your CHEM1B-AL health? 9 5
Chemistry 1B Fall 016 quatum mechaics of the hydroge atom (the electro waves i H atom ad their physical meaig) eergies of hydroge orbitals quatum umbers of allowed orbitals table 1. ad 1.3 orbitals ad the electro desity diagram orbital (wavefuctio, ) [ ca have relative sig, ± values] electro desity (probability, ) [ 0] radial probability distributio (4r ) Fig 1-16 & 1-17 hadout figures orbital idetificatio team activity Friday, 7 October 31 me Z Z E=- =-.178 10 J for H atom, Z=1 i hydroge atom, eergy oly depeds o quatum umber Fig. 1.3 4-18 80 h the size of the orbital is approximated by 11 ravg r a0 (5.910 m) Z Z (where a is a costat, the Bohr radius) 0 3 segue/review shapes of orbitals odal surfaces (idetifyig orbitals) 1.,,m possible allowed states waves for a electro i H atom radial ad agular odes of atomic orbitals. Allowed values of,, m 18 Z 3. E.17810 J Z 1 for H atom states of give but various, m have same eergy (are degeerate) 4. Shapes of orbitals,,, 4r - -1 radial (spherical) odes agular (plaar) odes 5. use rbohr ravg 11 r a0 (5.9 10 m) Z Z r a most probable 0 1 1 [ actually : r a0 1 1 Z 33 radial ode: a spherical shell (of radius r) where =0 (ad =0) ; has differet sig o opposite sides of radial ode agular ode: a surface (plae) where =0 (ad =0); has differet sig o opposite sides of agular ode d rules!! a orbital with quatum umbers,, m will have --1 radial odes agular odes -1 total odes ad +1 compoets i differet orietatios (from the differet possible m values) hold your horses 34 shapes of orbitals properties associated with,, m (HW# Prob x) radial ad agular odes s-orbitals Fig. 1.18 p-orbitals Fig. 1.19 & 1.0 d-orbitals Fig. 1.1 orbital pics i hadouts eergy radial ad total odes average distace from the ucleus agular velocity (agular mometum) shape (agular odal plaes ) WWW orbital viewers m orietatio of orbital 35 36 6
Chemistry 1B Fall 016 a sightig!!!!!! o ot alies!!! just d-orbital electros 37 38 Zuo, Kim, O Keeffe ad Spece, Nature, 1999. Larse 39 40 the sig of http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/ WHEW!!!, the orbital or wave fuctio, ca have differig sigs i differig spatial regios; but, the probability of fidig a electro at a positio, is always positive I goig betwee + ad regios there will be a place where =0. This is a ode of the orbital. ed of lectures 3-4 41 Does the of idicate regios of + charge ad charge? NO!!! Repeat after me: The + or regios of DO NOT correspod to regios of positive ad egative charge, but just to the relative sig of the wavefuctio!! 4 7
Chemistry 1B Fall 016 Zumdahl: figure 1.16-17 Silberberg: figure 7.16 Silberberg: figure 7.16 R ºY R ºY radial probability 4r cotour 43 = probability desity i small volume at (x,y,z) [(r,,)] probability of fidig electro at positio (r,,) 4r = radial probability add up desity i ALL small volumes at distace r total probability desity i small spherical shell at distace r from ucleus probability of fidig electro at r (irrespective of its ad ) 44 90 % cotour with sig represetatios of orbitals cotour with sig Zumdahl: figure 1.3 + vs r - + desity of dots vs r probability 3-D shadig desity of dots r radial probability r vs r 45 46 Zumdahl Tables 1. ad 1.3 Zumdahl: figure 1.18 ad Silberberg: figure 7.17 47 48 8
Chemistry 1B Fall 016 Zumdahl Figs 1-19, 1-0 Silberberg: figure 7.18 ( ) ( ) ( ) 0 6 4 8 0 4 6 8 10 1 14 (sum of all ) (sum of all ) 6 8 s orbital (sum of all ) 4 6 8 10 0 1 14 3s orbital 49 1 agular 3p x x 50 Zumdahl figure 1.1 Silberberg: figure 7.19 --1=3--1=0 radial odes y z x x 3d xy 3d x-y 3d z 51 5 Silberberg Table 7.1 Ucertaity ad measuremet ote mass i g, eed to use kg for mvl=h (l correct i table) 53 54 9
Chemistry 1B Fall 016 ( ) ( ) (sum of all ) (sum of all ) 55 56 ( ) ( ) ( ) ( ) 0 6 4 8 0 6 4 8 (sum of all ) (sum of all ) 6 8 s orbital 57 (sum of all ) (sum of all ) 6 8 s orbital 58 ( ) ( ) ( ) ( ) ( ) 0 6 4 8 0 6 4 8 0 4 6 8 10 1 14 (sum of all ) (sum of all ) 6 8 s orbital 59 (sum of all ) (sum of all ) (sum of all ) 6 8 4 6 8 10 0 1 14 s orbital 3s orbital 60 10
Chemistry 1B Fall 016 ( ) ( ) ( ) ( ) ( ) ( ) 0 6 4 8 0 4 6 8 10 1 14 0 6 4 8 0 4 6 8 10 1 14 (sum of all ) (sum of all ) (sum of all ) 6 8 4 6 8 10 0 1 14 s orbital 3s orbital 61 (sum of all ) (sum of all ) 6 8 s orbital (sum of all ) 4 6 8 10 0 1 14 3s orbital 6 11