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ELECTRONIC STRUCTURE

ELECTRONIC STRUCTURE. Electromagnetic Radiation. Bohr Model. Rydberg Eqn & Constant. E-Levels; quantum #’s. Planck’s Eqn & Constant. Ionization E. Classic Physics - wave vs particle. de Broglie Wavelength Heisenberg Uncertainty Principle. Quantum Mechanics

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ELECTRONIC STRUCTURE

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  1. ELECTRONIC STRUCTURE Electromagnetic Radiation Bohr Model Rydberg Eqn & Constant E-Levels; quantum #’s Planck’s Eqn & Constant Ionization E Classic Physics - wave vs particle de Broglie Wavelength Heisenberg Uncertainty Principle Quantum Mechanics Orbital Shapes

  2. Quantum Theory: aids to explain behavior of e- describes e- arrangement in atoms Classical Physics + nucleus === - e- ∆: smooth continuous spectra

  3. , nm 106 1012 104 10-2 102 V I S  RAYS U V I R MICRO 1020 1016 1011 105 1013 , s-1 Electromagnetic Radiation: consists of E by means of electrical & magnetic fields; inc/dec intensity as move thru space 400 500 750 V I B G. Y O R 7.5*1014 6.0*1014 4.0*1014

  4. WAVE PROPERTIES 2 Independent Variables Frequency, : cycles /s, 1/s --- s-1 (Hertz) Wavelength, : dist bet crest or trough of a wave dist in 1 cycle m, nm (109 nm = 1 m), pm, Å In vacuum all electromag radiation same speed 3.00*108 m/s === speed of light (c) c = * radiation wavelength higher , shorter Amplitude: height of crest; depth of trough - higher amp, increase intensity - measure strength of fields

  5. amplitude

  6. Max Planck --- Planck’s Constant E = nh n: quantum #; 1, 2, 3, … h: constant 6.626*10-34 J-s : frequency E of atom is quantized; specific amts quantum: fixed amt of E required to move e- to next E-level quantum = h Einstein Photon: quantized bundles of E; light - behaves as a particle

  7. Calculate E from  c =  ==  = c/ E = nh = h = h(c/ ) n= 1 & : m Sr Photoelectric Effect: light delivering E fixed amts; supports E-levels & quantum model of atom; light dual nature, behaves as waves & composed of particles Light shining on metallic surface will emit e- if min. light frequency is met

  8. Calculate wavelength of yellow light that emits a frequency of 5.10*1014 s-1.  = c/ 5.88 * 10-7 m Calculate the E, J, of a quantum of E w/ a frequency of 5.00 * 1015 s-1. E = h *  E = (6.626 * 10-34 J-s) (5.00 * 1015 s-1) = 3.31 * 10-18 J

  9. ATOMIC SPECTRA Ryberg Eqn -- Rydberg Constant 1.097*107 m-1 n2 > n1 n1 = 2 visible series BOHR MODEL --- H atom 3 Postulates - Atom certain allowable E-levels (stationary states) - Atom not emit E in stationary state - Atom ∆es states when +/- photon of = difference of E bet 2 states Ephoton = Estate 2 – Estate 1 = h emit specific quantum of E

  10. n: quantum #, 1, 2, 3, …. n = 1 smallest atomic radius smallest E-level e- location: lowest E-level is ground state e- + photon; photon E match diff bet n1 & n2; e- moves to 2nd E-level, excited state; (any higher E-level above ground state) e- emits same amt E as absorbed from photon; moves (falls) back to ground state E-level Calculate E-levels E = -2.18*10-18 J *(Z2/n2) Z: + charge on nucleus n: quantum #, ground state

  11.  1016 1015 1014 3 groups of lines H spectrum Lyman Series UV Balmer Series VIS Paschen Series IR nn ---> n1 nn ---> n2 nn ---> n3

  12. Diff 2 E-levels Combine ∆E w/ Planck’s === Rydberg’s Eqn IONIZE H H (g) ---- H+(g) + e- ni = 1 nf = ∞

  13. amt E absorbed, +, to completely remove 1 e- What is the E of an e- in the 2nd E-level? -5.45 * 10-19 J What is the E required to excited e- from n=1 to n=2? E = E2 - E1 1.63*10-18 J = (-5.45*10-19) - (-2.18*10-18) =

  14. Calculate the wavelength (nm) of the line in the spectrum (H) corresponding to n1 = 2 to n2 = 4 Ryberg Eqn 1.097*107 m-1 (4.862*10-7 m)*(1 nm/1*10-9 m) = 486 nm Calculate the E emitted from a hydrogen atom when an e- drops from 5th to 2nd E-level. Calculate frequency (Hz) & wavelength (nm). E = h  = E/h 4.58*10-19 J 6.91*1014 s-1 434 nm c = /  = c/

  15. 1905 -- Einstein -- E=mc2 matter & E are alternate forms of same E is particle; physicists matter is wave-like Bohr Model atom only has certain allowable E-levels explain line spectrum de Broglie study of systems w/ only allowable motions extended this reasoning to e- behave wave-like, restricted to fixed radii explain why e- certain E’s & freq.

  16. de Broglie combined: E=mc2 & E=h=hc/ eqn for  of any particle w/ mass (m) @ speed u Matter moves in a wave  inverse to its mass, therefore, heavy objects, their  <<<<< smaller Question was asked: if e- have properties of E, do photons have properties of matter? Can calculate the momentum (p)

  17. Calculate the  for an e- (9.11*10-31 kg) w/ speed of 1.0*107 m/s. 6.626 * 10-34 J/s ====> 6.626*10-34 kg-m2/s 7.27*10-11 m

  18. HEISENBERGUNCERTAINTY PRINCIPLE Classical sense; moving particle has definite position know path & location of an object Postulated that --- if e- is both particle and wave like, then impossible to know position & momentum of e- at the same time more know position, less know of speed Outcome for Atomic Model Not assign fixed orbit; as Bohr model shows Can state is the probability of e- in a given region; but still not sure??

  19. PAULI EXCLUSION PRINCIPLE An orbital can hold only 2 e-’s & the 2 e-’s must have opposite spin An orbital occupied by 2 e-’s w/ opposite spin is filled 2 Hydrogen atoms 1s1 & 1s1 H -- H Will these 2 hydrogen atoms bond together ????? Only if the 1s e-’s are of opposite spin 2 e-’s w/ same spin direction cannot occupy same region of space

  20. e- structure e- locate: outside of nucleus e- cloud, shell, “subshell”, orbital, E-level E is quantized; a specific value Shell ( E Level) 1st: closest to nucleus, lowest in E 7th: farthest from nucleus, highest in E w/i shells are “subshells” s, p, d, f w/i subshells are orbitials geometric shaped regions where the high probability to locate e- exists

  21. Shell subshell orbitial max. e- 1 2 3 4 5 6 7 s s, p s, p, d s, p, s, p, s, p, d s, p d, f d, f 1 1-3 1-3-5 1-3-5-7 1-3-5-7 1-3-5 1-3 2 2-6 2-6-10 2-6- 2-6- 2-6-10 2-6 10-14 10-14 s: 1st 2 elements of each row; 1 pair, 2 e-; 1A - 2A p: last 6 elements of each row; 3 pair, 6 e-; 3A - 8A d: transition elements; 5 pair, 10 e-; B f: rare earth elements; 7 pair, 14 e-; not labeled

  22. How many e- are present, group by E-levels He Be N F Na Al 1st ---> 2e- 1st ---> 2e- 2nd ---> 2e- 1st ---> 2e- 2nd ---> 5 e- 1st ---> 2e- 2nd ---> 7 e- 1st ---> 2e- 2nd ---> 8 e- 3rd ---> 1 e- 1st ---> 2e- 2nd ---> 8 e- 3rd ---> 3 e-

  23. Now, identify e- by subshells He Be N F Na Al 1st :2e- s 1st:2e- 2nd:2e- s s 1st:2e- 2nd:5 e- s s, p 1st:2e- 2nd:7 e- s s, p 1st:2e- 2nd:8 e- 3rd:1 e- s s, p s 1st:2e- 2nd:8 e- 3rd:3 e- s s, p s, p

  24. 1 2 3 4 5 6 7 <-------------------------1s------------------------------------------------> <-2s-> <--2p------------------> <-3s-> <-----3p---------------> <-4s-> <--------4p------------> <-------3d--------------------------> <-5s-> <-------------5p---------> <------------4d--------------------> <-6s-> <---------------6p-----> <----------------5d----------------> <--------------------6d------------> <-7s-> <------------------7p--> <-------------4f----------------------------------------> <----------------------5f------------------------------->

  25. E- Notation # e- Form: 1s2 subshell E-level “shell” Be N F Na Al 1s22s2 Ca 1s22s2p3 1s22s22p3 1s22s2p63s2p64s2 1s22s2p5 1s22s22p5 1s22s22p63s1 1s22s2p63s1 1s22s2p63s2p1 1s22s22p63s23p1

  26. After 4s2, 3d level fills till 3d10 completed, then complete 4p 4p to 5s, 4d completed, then complete 5p 5p to 6s, 4f level fills till 4f14 completed, then start 5d to 6p Mn 1s22s2p63s2p64s23d5 Zn 1s22s2p63s2p64s23d10 Ga 1s22s2p63s2p64s23d104p1 Pd-46 1s22s2p63s2p64s23d104p65s24d8 Nd 1s22s2p63s2p64s23d104p65s24d105p66s25d14f3

  27. Group E-levels Order e- Filling Short-cut 1s22s2p63s2p6d104s2p6d10f35s2p6d1 6s2 1s22s2p63s2p64s23d104p65s24d105p66s25d14f3 1s22s2p63s2p64s23d104p65s24d105p66s25d14f3 this is added on to the noble gas notation describes noble gas @ end of row 5 (Xe) filled inner core of e- [Xe]4f35d1 6s2 Valance e- (2) total # of e- in highest E-level methods easiest to show # val. e-

  28. RULES & PRINCIPLES HUND’S RULE Describes the lowest E arrangement of e- Based on results of measurements of magnetic properties 1. e- enter orbital of same E singularly till orbital half filled • Each orbital must be occupied with an e- w/ parallel • spin direction before e-’s are paired w/ opposite spin

  29. FILLING ORBITALS S 1s22s2p63s2p4 3s p 4 2 pX pY pZ 3 s Valence e- level 6 valence e-’s 2s p 2 pX pY 6 pZ 2 s 1s 2 1 s

  30. FILLING ORBITALS Cr 1s22s2p63s2p6d54s1 1 valence electron 4s 4 1 2 s d d d d d 3s p d 2 6 4 5 pX pY pZ 3 s 2s p 2 6 pX pY pZ 2 s 1s 2 1 s

  31. What Element??? Atom?? 1s22s2p63s2p6 4 3 s d d d d d 4 s pX pY pZ 3 s pX pY pZ 2 s 1 s Ni Nickel 3 d d d d d

  32. PRACTICE PROBLEMS Write electron notation, long & short, for: Cobalt - Silver - I-1 ion Draw orbital diagram for Cobalt Identify the following elements: 1s22s2p63s2p64s23d104p5 1s22s2p63s2p6d104s2p6d75s2 Identify the number of valence electrons in each element

  33. 2 n=1 Dist -----------------------> QUANTUM MECHANICS Schrödinger Eqn: used to describe model for H atom - certain allowabel E - wave behavior - e- position not known E: E of e- : psi, wave fct H: Hamiltonian Operator  has no meaning, but, 2 is probability density

  34. 3 QUANTUM NUMBERS 1 SIZE 2 SHAPE 3 ORIENTATION 1 Principal QN (n); + integer 1, 2, 3, …. identify E-level indicates size due from probability distr 2 Angular Momentum QN (l); 0 to (n-1) shape n limits l amt of l values = n n = 1 l = 0 n = 2 l = 0, 1 n = 5 l = 4, 3, 2, 1, 0

  35. 3 Magnetic QN (ml);-1, 0, +1 shows orientation of orbitals around the nucleus l sets the ml values l = 0 then ml = 0 l = 1 then ml= -l, 0, +l # of ml values = # of orbitals; 2l + 1 l = 2 ml = -2, -1, 0, +1, +2 H Atom Summary 1. In quantum (wave) model, e- a standing wave. Leads to series of wave fcts (orbitals) describe possible E & spatial distributions 2. As w/ Heisenberg, model cannot detail e- motions. But, the 2 shows probability distr of e- in that orbital (e- density maps) 3. Orbital size defined as surface that contains 90% of total e- probability 4. H atom many types of orbitals. Ground state is 1s, but can be excited w/ input of min E requirement

  36. # of orbitals n= n2 l Sublevels (subshells) s, p, d, f l=0l=1l=2l=3 n Level: E-level (shells) orbitals n=1 l=0 1s 2s: n= l= 2p: n= l= 3s: n= l= 3p: n= l= 3d: n= l= 2021 3031 32

  37. l = 0 then ml = 0 l = 1 then ml = -1, 0, +1 l = 2 then ml = -2, -1, 0, +1, +2 S Px, Py, Pz dxy, dyz, dz2, dxz, dx2-y2 n l m describes ? ? 0 4p 2 1 0 ? 3 2 -2 ? ? ? ? 2s 4 1 2p 3d 2 0 0

  38. p orbitals dumb bell shaped 2 regions either side of nucleus of high probability 2p: n = 2 l = 1 ml = -1, 0, +1 Px Py Pz d orbitals dumb bell shaped; dz2: disc shape bet dumb bells orbital s p d f l = 0 l = 1 l = 2 l = 3

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