CHAPTER 6:

1. CHAPTER 6: ELECTRONIC STRUCTURE

2. The Nature of Light • Quantized Energy/Photons • Photoelectric Effect • Bohr’s Model of Hydrogen • Wave Behavior of Matter • Uncertainty Principle • Quantum Mechanics/Atomic Orbitals • Quantum Numbers/Orbitals

3. Representations of Orbitals • Many-Electron Atoms • Effective Nuclear Charge • Relative Energies of Orbitals • Electron Spin/Pauli Excl. Principle • Electron Configurations • Periodic Relationships

4. Wave Nature of Light Electromagnetic Radiation • electric & magnetic components with periodic oscillations • length in m, cm, mm, mm, nm, l • frequency in cycles/sec or hertz, n • nl = c where c = speed of light

5. l long wavelength l short wavelength

6. Quantized Energy and Photons Black Body Radiation • heated bodies radiate light and l depends on temperature • Planck -- energy released in ‘packets’ • smallest ‘packet’ is a quantum • energy of one quantum , E = hn • h, Planck’s constant = 6.63 x 10 - 34 J-s

7. Practice Ex. 6.2: A laser that emits light in short pulses has a n = 4.69 x 1014 s-1and deposits 1.3 x 10 -2 J of energy during each pulse. How many quanta of energy does each pulse deposit? • E = hn • E of 1 quantum = (6.63 x 10 -34 J-s) (4.69 x 1014 s-1) =3.11 x 10 -19 J/quanta • 1.3 x 10 -2 J = 4.2 x 10 16 quanta 3.11 x 10 -19 J/quanta

8. Photoelectric Effect • metals exposed to light, radiant energy, emit electrons • each metal has a minimum n of light • Einstein’s ‘photons’ of light must have sufficient threshold energy • energy of photon depends on the n of light, E = hn • high frequency, short wavelength(l = c/n) µhigh energy • light is also quantized, 1 photon = 1 quanta

9. photon with E > threshold e - with kinetic energy = photon E - threshold E e - metal surface

10. Bohr’s Model of the Hydrogen Atom Line Spectra • spectrum -- light composed of different wavelengths and energies • contiunous spectrum -- continuous range ofl’s and E’s • line spectrum -- non-continuous spectrum (only specificl’s and E’s) • Balmer 1800’sn = C (1/22 - 1/n2)n = 3, 4, 5, 6 C = 3.29 x 10 15 s - 1

11. Hydrogen Line Spectrum 400 450 500 550 600

12. Bohr’s Model • electrons in “orbits” around nucleus • “orbits” are allowed energies which are quantized • to move between quantized orbits, electrons must either absorb or emit quanta of energy • E = - RH ( 1/n2 ) n = 1, 2, 3, 4 . . . . . principle quantum number • RH(Rydberg constant)= 2.18 x 10 -18 J

13. nucleus e- e- e- Energy absorption n=1 n=2 n=3 n=4

14. e- Energy emission e- nucleus n=1 n=2 n=3 n=4

15. DE = Ef - Ei = hn DE1 > DE2 > DE3 DE3 DE2 e- DE1 e- nucleus n=1 n=4 n=3 n=2

16. energy of the transition depends on the levels DE = Ef - Ei = hn or DE = n = Ef - Eih • n = (RH/h )(1/ni2 - 1/nf2) or DE = RH (1/ni2 - 1/nf2) • ni = initial level of electron • nf = final level of electron

17. DE or n is +radiant energy absorbed DE or n is -radiant energy emitted nucleus n=1 n=2 n=3 n=4

18. Balmer Series - visible H line spectrum Lyman Series - in the uv H 2 3 4 5 n=1 6

20. Wave Behavior of Matter Basis for Quantum Mechanics • De Broglie wave equation • l = h“matter” waves mv • Uncertainty Principle -- Werner Heisenberg • fundamental limitation on how precisely we can know the locationand momentum

21. Quantum Mechanics and Atomic Orbitals Quantum Mechanics or Wave Mechanics • mathematical method of predicting the behavior of electrons • wave functions are solutions to these mathematical equations • wave functions predict the “probability” of finding electron density, Y2 • wavefunction describes “orbitals”

22. Orbitals & Quantum Numbers • orbitals describe volumes of electron density • orbitals are of different types s, p, d, f • each orbital is described by a set of quantum numbers n,l, m • each quantum number has an allowed set of values

23. Quantum Numbers nÞ can have values of 1, 2, 3, 4, 5 . . . . • describes the major shell or distance from the nucleus lÞ can have values of 0, 1, 2, 3 . . . n-1 • describes the type of subshell • l = 0 s subshelll = 1 p subshell • l = 2 d subshell l = 3 f subshell mÞ can have values of - l . . . 0 . . . + l • describes which orbital within the subshell

24. s p p l = 0 p s s d l = 1 p d p p d l = 2 p d d d s l = 3 f d f p d f p d f p d s f d f f nucleus f + n=1 n=2 n=3 n=4

25. total number of orbitals in a subshell is n2 • maximum number of electrons in a subshell is 2n2 • maximum number of electrons in an orbital is 2 s Þ last quantum number describes the spin on an electron • each electron has a spin +½ or -½

26. s p p l = 0 p s s d l = 1 p d p p d l = 2 p d d m d s -2 m l = 3 m f d -1 -3 -1 f p d -2 0 0 f p d m -1 +1 f +1 p d 0 0 s +2 f d +1 f +2 f nucleus +3 f + n=1 n=2 n=3 n=4

27. Orbital Pictures s-type orbitals • always oneorbital in the subshell with l = 0 and m = 0 • are spherical • differences between s orbitals in different major shells (with different n values) • size • remember, we’re talking in terms of probability of the occurrence of electron density

28. Notice that we are looking at a volume of diffuse electron electron density as pictured by the many small dots

29. s orbital cross-sections

30. p-type orbitals • always three orbitals in the subshell with l = 1 and m = -1, 0, +1 • are dumb-bell shaped • different m values are oriented along different axes, x, y, or z (px, py, pz) • differences between p orbitals in different major shells • size

32. d-type orbitals • always five orbitals in the subshell with l = 2 and m = -2, -1, 0 +1, +2 • most are four-lobed • different m values are oriented differently on x, y, z axes dz2, dx2-y2, dxy, dxz, dyz • differences between d orbitals in different major shells • size

34. n=4 p p d d d d f f f f f f p d f s n=3 s p p d d d d p d n=2 s p p p Orbital/Subshell energy levels in the hydrogen atom n=1 s Energy

35. Multi-electron Atoms screening effect • inner electrons “shield” the nuclear charge from outer electrons • energy levels of subshells within major shells become different • nuclear charge experience by outer electrons is decreased • Zeff = Z - S • Zeff decreases withincreasingl value

36. n=3 d d d d d n=3 p p p n=3 s n=2 p p p n=2 s Orbital/Subshell energy levels in multi electron atoms n=1 s Energy

37. p p p Pauli Exclusion Principle • no two electrons can have the same exact set of quantum numbers • consider this orbital and its two electrons • quantum numbers aren = 2, l = 1, m = 0 • the two electrons must have a quantum number that is different -- s = +½ and - ½ • First electron has spin +½ and second electron -½ n=2 l = 1m = -1 0 +1

38. Electron Configurations There is a pattern in the energy levels that hold electrons • electrons fill up the pattern from the lowest energy to the highest energy level • 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s • for 1H ­ for 2He ­¯ 1s 1s • 3Li ­¯­4Be ­¯ ­¯ 1s 2s 1s 2s

39. Hund’s Rule • electrons enter degenerate orbitals in a subshell one at a time until the subshell is half-filled • 5B ­¯ ­¯­6C ­¯­¯­­ 1s 2s 2p 1s 2s 2p • 7N ­¯­¯­­­ 1s 2s 2p • 8O ­¯­¯­¯­­ 1s 2s 2p

40. Periods 1, 2 & 3 • 3Li­¯­ 1s 2s • 11Na ­¯­¯­¯­¯­¯­ 1s 2s 2p 3s • 19K ­¯­¯­¯­¯­¯­¯ ­¯­¯­¯­ 1s 2s 2p 3s 3p 4s • outer shell is called thevalence shell

41. Group 1 • 3Li­¯­ 1s 2s • 11Na ­¯­¯­¯­¯­¯­ 1s 2s 2p 3s • 19K ­¯­¯­¯­¯­¯­¯ ­¯­¯­¯­ 1s 2s 2p 3s 3p 4s [Ne] 3s1 [Ne] [Ar] [Ar]4s1

42. all group I elements have electron configuration • [nobel gas] ns1 • all group II elements have electron configuration • [nobel gas] ns2 • all group III elements have electron configuration • [nobel gas] ns2 np1 • group IV elements • [nobel gas] ns2 np2 • group V elements • [novel gas] ns2 np3 etc.

43. d1 . . . . . . . . . . . . . . d10 1 2 3 4 5 6 7 8 ns2p6 ns1 1 2 3 4 5 6 7 ns2p1 ns2p2 ns2p3 ns2p4 ns2p5 ns2 s1 s2 p3 p4 p5 p6 p7 p8 ns2 (n-1)d1-10 Electron Configuration & Periodic Table