sessions lectures 3-4

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$17810 J 1 1 7 1 1 1 Z 1. 0967 10 m Z hc 1 1 (537-54, *(543-549), 549-557) 1 wave-particle duality diffractio of electros- (Davisso-Germer Experimet; p. 530) De Broglie relatioship (p. 58) (HW#1 1.3,1.$ 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.

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.

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.

1 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 J Z=1 for H atom, =1,, 3, J Z m Z hc 1 1 (537-54, *( ), ) 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?? ( ( 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

Chemistry 1B Fall 016 quatum mechaics: WEIRD Quatum Jujitsu π Quatum Mechaics 7 8 what quatum mechaics must iclude goals of lectures 3-4

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

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?

9 10 Bohr model vs Quatum Bohr model got the eergies of allowed levels correctly However Bohr model assumed electros travelig aroud

ad Heiseberg Ucertaity Priciple Schrödiger equatio (see pp 540 ad 549) SCHRÖDINGER EQUATION H E m V E basic equatio of quatum mechaics

2 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. ( )*, Table 1.1 1

3 Chemistry 1B Fall 016 hydroge s electro waves: the three quatum umbers (pp ) 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**** 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. ( )*, Table hydroge s electro waves: the three quatum umbers (pp ) hydroge s electro waves: the three quatum umbers (pp ) 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

Chemistry 1B Fall 016 rules for allowed quatum umbers rules for allowed quatum

..., positive, o-zero, itegers agular mometum quatum umber for give value of = 0, 1,,.

mometum quatum umber desigatios of orbitals with various values of 0 1 3.

. from spectroscopy sharp pricipal diffuse fudametal 1 HW#1 10, 11, 1 rules for

4 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 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,

quatum umbers of allowed orbitals table 1. ad 1.

5 Chemistry 1B Fall 016 Zumdahl Tables 1. ad 1.3 HW#1 10, 11, 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

6 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=- = J for H atom, Z=1 i hydroge atom, eergy oly depeds o quatum umber Fig 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 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 ( m) Z Z r a most probable [ 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 p-orbitals Fig & 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

Chemistry 1B Fall 016 a sightig!!!!!! o ot alies!

Larse 39 40 the sig of http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/ WHEW!

but, the probability of fidig a electro at a positio, is always positive I goig

ed of lectures 3-4 41 Does the of idicate regios of + charge ad charge? NO!

7 Chemistry 1B Fall 016 a sightig!!!!!! o ot alies!!! just d-orbital electros Zuo, Kim, O Keeffe ad Spece, Nature, Larse the sig of 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 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

8 Chemistry 1B Fall 016 Zumdahl: figure 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 ) % cotour with sig represetatios of orbitals cotour with sig Zumdahl: figure vs r - + desity of dots vs r probability 3-D shadig desity of dots r radial probability r vs r Zumdahl Tables 1. ad 1.3 Zumdahl: figure 1.18 ad Silberberg: figure

9 Chemistry 1B Fall 016 Zumdahl Figs 1-19, 1-0 Silberberg: figure 7.18 ( ) ( ) ( ) (sum of all ) (sum of all ) 6 8 s orbital (sum of all ) s orbital 49 1 agular 3p x x 50 Zumdahl figure 1.1 Silberberg: figure =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)

10 Chemistry 1B Fall 016 ( ) ( ) (sum of all ) (sum of all ) ( ) ( ) ( ) ( ) (sum of all ) (sum of all ) 6 8 s orbital 57 (sum of all ) (sum of all ) 6 8 s orbital 58 ( ) ( ) ( ) ( ) ( ) (sum of all ) (sum of all ) 6 8 s orbital 59 (sum of all ) (sum of all ) (sum of all ) s orbital 3s orbital 60 10

11 Chemistry 1B Fall 016 ( ) ( ) ( ) ( ) ( ) ( ) (sum of all ) (sum of all ) (sum of all ) s orbital 3s orbital 61 (sum of all ) (sum of all ) 6 8 s orbital (sum of all ) s orbital 6 11

sessions lectures 3-4

Chemistry 1B Fall 2016 sessions lectures 3-4 (537-542, *(543-549), 549-557) 1 quantization of energy E photon = h absorption and emission spectra of hydrogen atom 2 18 Z En 2. 17810 J 2 n Z=1 for H atom,