Quantum Theory of the Atom. Description of the atom and subatomic particles. We will focus on the electronic structure of the atom.

Transcription

1 Quantum Theory of the Atom Description of the atom and subatomic particles. We will focus on the electronic structure of the atom. 1

2 Classical Quantum 1900: Max Planck (studying radiation from heated objects) discovered energy is emitted in quanta, 2

3 Background: Waves Light energy travels in waves. Sine (or cosine) waveform Wavelength: l Frequency: n Energy: E 3

4 Waves Frequency (n) is number waves/sec (cycles per second = Hz) 4

5 Wave Speed: u u = l n length time m/s length wave m waves time s -1 = Hz Ocean: energy moves, not water! 5

6 n (Hz) l (m) Electromagnetic Radiation Light is EM wave u = c = 3.00 x 10 8 m/s 6

7 Electromagnetic Radiation What is the frequency of green light with l = 522 nm? u = c = l n n = c/l n = (3 x10 8 m/s) / 522 x 10-9 m = 5.75 X Hz 7

8 Electromagnetic Radiation Try it: What is wavelength in nm of radio waves with frequency of 5.2 x 10 6 Hz? 8

9 EM Radiation (light) Light: wave or particle? Yes! Excerpt from Physics by Giancolli Photon: smallest particle of light. 9

10 Energy of a Photon Energy (E) is proportional to n E = h n Planck s constant= 6.63 x J s Light emitted in energy packets of hn. This equation links wave and particle theory. 10

11 E = h n What is the energy of a yellow photon with frequency of 6.12 x Hz? 11

12 Energy of a Photon Since and E = h n c = l n then E = hc l 12

13 E = hc l Try it: What is the energy of a blue photon with a wavelength of 420 nm? 13

14 E = hc l Keep going: What is the energy of a mole of blue photons with a wavelength of 420 nm? 14

15 1913: The Bohr Hydrogen Atom 15

16 What Holds an Electron Near the Nucleus? Classical physics: Electrostatic attraction F = q 1 q 2 r 2 Coulomb s Law q 1 =nuclear charge (+) q 2 = electron charge (-) r = distance between nucleus & e - 16

17 Emission Spectrum Excited atoms are known to emit energy in the form of discrete wavelengths of light. Why?? 17

18 Hydrogen Line Spectrum 18

19 Bohr: Planetary Model Electrons move in circular orbits around nucleus, and each orbit has a certain energy. E, E, E e - energy is quantized 19

20 energy Stair Analogy: H spectrum due to e - transition between orbits. E 5 E 4 E 3 E 2 E 1 20

21 energy e - in Ground State E 5 E 4 E 3 E 2 E 1 21

22 energy e - in Excited State E 5 E 4 Is e - moving to excited state endo- or exothermic? E 3 E 2 E 1 22

23 energy e - in Excited State E 5 E 4 E 3 E 2 E 1 23

24 energy e - Returning to Ground E 5 E 4 photon E 3 E 2 Endo- or exothermic? E 1 24

25 energy e - Returning to Ground E 5 E 4 lower energy photon E 3 E 2 E 1 25

26 Bohr: Hydrogen Emission Spectrum E 3 E 2 E 1 + e - absorbs energy (heat, elec.) e - falls to lower E and gives off energy as light E light =E 3 -E 1 26

27 Bohr: Hydrogen Emission Spectrum 27

28 Bohr: Energy Levels (H only) E n = x J n 2 1 n is the e - energy level or orbit n = 1, 2, 3, (quantized) Negative since free electron is defined as zero energy. 28

29 Photon Energy (line emission) DE = hn = hc/l = E f - E i hc/l = -2.18E-18 J 1 n f 2-1 n i 2 (allows calculation of the wavelengths of hydrogen spectrum) 29

30 Try it! What is the wavelength of a light emitted from transition of e- from 5 th energy level to ground state (n=1)? What part of the EM spectrum is this photon? 30

31 Emission of Light 31

32 Bohr Theory: Failings 1.What holds an electron in an orbit? 2.Why do e - only have certain orbital energies? 3.Only explains hydrogen. 32

33 DeBroglie: 1924 e - is both particle and wave (WOW!), and orbits must be quantized to fit the e - wave. (You are also particle & wave!!!) 33

34 Electrons as Waves n =4.3 n = 5 n = 4 34

35 Electrons as Waves 2pr = n l quantization 35

36 Quantum Mechanics (Wave Mechanics) 1926: Erwin Schrodinger and Werner Heisenberg e - location (orbital) only described by a probability function, Y. 36

37 Schrodinger Equation d 2 Y dx 2 + d2 Y dy 2 d 2 Y + + dz 2 8p 2 m h 2 (E U) Y = 0 37

38 Quantum Mechanics The Schrodinger equation can only be solved exactly for H atom. Other atoms can be solved by approximation. 38

39 Electron Orbitals e - do not revolve in orbits. Orbital: region in space around the nucleus with high probability of finding an e -. Each orbital can hold two e -. 95% 39

40 Electron Orbitals: given by 3 quantum numbers Principal QN = n = shell overall e - energy Angular momentum QN = subshell orbital shape Magnetic QN direction in space of the orbital 40

41 Principal Quantum Number (n) or Principal Energy Shell n = 1, 2, 3, 4, 5 (integer values) Gives overall energy of an e - and its distance from nucleus. 41

42 Angular momentum QN (subshell) Gives shape of the e - cloud designated by letters: s, p, d, f 42

43 Energy Subshell s has 1 orbital p has 3 orbitals d has 5 orbitals f has 7 orbitals 2 e - 6 e - 10 e - 14 e - Each orbital can hold 2 e - 43

44 s orbitals (one per energy level) 1s 2s 3s 44

45 p orbitals (three per energy level) p x p y p z 45

46 d orbitals (five per energy level) d xz d yz d xy d x 2-y2 d z 2 46

47 f orbitals (seven per energy level) 47

48 Number of Orbitals per energy level one s three p five d seven f 48

49 Allowed Combinations n Sublevels # Orbitals #e 1 1s s 2p 1+3= s 3p 3d 1+3+5= s 4p 4d 4f =16 32 (model) 49

50 e - Configurations: 3 Rules 1. Aufbau: arrange e - by lowest energy level first 2. Pauli Exclusion Principle: only 2 e - per orbital 3. Hund s Rule: maximize the number of parallel spin e - when filling a sublevel 50

51 Aufbau: Electron Energy For Hydrogen, n alone determines the energy level. Thus: E 1s<2s=2p<3s =3p=3d<4s.. 51

52 Electron Energy In all atoms but hydrogen, the energy of an e - in an orbital depends on both level & sublevel. 52

53 Energy & Shielding In many-electron atoms, inner shell e - reduce the positive nuclear charge felt by outer e -. Z = nuclear charge = +3 Z eff = effective nuclear charge is closer to +1 2s 1s Li +3 53

54 Shielding Due to different orbital shapes, a 2s e - has slightly greater e - density nearer the nucleus than a 2p e -. Thus 2s has lower energy than 2p, and 2s shields 2p. 54

55 Shielding n = 4 s d n = 3 p s n = 2 p s n = 1 s 55

56 Energy Levels Order of increasing energy: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s lower than 3d!! 56

57 Orbital Box Diagram energy 1s 2s 2p 3s 3p 4s 3d 4p 5s 57

58 2. Pauli Exclusion Principle: only 2 e - per orbital Electrons have spin! 1s orbital Paired electrons: e - in an orbital have opposite spins 58

59 3. Hund s Rule Maximize parallel (same) spins when filling a sublevel In a sublevel, put one e - in each orbital before pairing Example: 4 e - in a p sublevel 59

60 Overview _embedded&v=8rohpz0a70i#t=4 60

61 Hydrogen: 1 electron 1s 2s 2p 3s Recall for neutral atom #e - is same as # p + (atomic number). 61

62 Electron Configuration Hydrogen 1s # of e - s 1s 1 n sublevel 62

63 Helium: 2 electrons 1s 2s 2p 3s Notation: 1s 2 63

64 Lithium: 3 electrons 1s 2s 2p 3s Notation: 1s 2 2s 1 64

65 Boron: 5 electrons 1s 2s 2p 3s Notation: 1s 2 2s 2 2p 1 65

66 Nitrogen: 7 electrons 1s 2s 2p 3s Notation: 1s 2 2s 2 2p 3 66

67 Fluorine: 9 electrons 1s 2s 2p 3s Notation: 1s 2 2s 2 2p 5 67

68 Neon: 10 electrons 1s 2s 2p 3s Notation: 1s 2 2s 2 2p 6 68

69 Sodium: 11 electrons 1s 2s 2p 3s Notation: 1s 2 2s 2 2p 6 3s 1 69

70 Shorthand for Sodium 1s 2 2s 2 2p 6 3s 1 [Ne] 3s 1 Use the preceding [noble gas] 70

71 Third Period Same as Period 2 except e - are being added to n=3 Na, Mg, Al, Si, P, S, Cl, Ar Ar is 1s 2 2s 2 2p 6 3s 2 3p 6 71

72 Period 4 Elements K [Ar]4s 1 (recall 4s fills before 3d) Ca [Ar]4s 2 Sc [Ar]3d 1 4s 2 (1 st transition) note written order 72

73 Some More of Period 4 Ti [Ar]3d 2 4s 2 V [Ar]3d 3 4s 2 Cr [Ar]3d 5 4s 1 Mn [Ar]3d 5 4s 2 Cu [Ar]3d 10 4s 1 Zn [Ar]3d 10 4s 2 filled & half filled d-subshell stability 73

74 Half-Filled Rule In some atoms, completely filled and exactly half-filled d and f sublevels have additional stability (lower energy). This can happen because energy levels get closer together farther from the nucleus. 74

75 Two Exceptions in Row 4 Cr (Z= 24) [Ar] 4s 3d [Ar] half-filled stability 75

76 2nd Exception Cu (Z= 29) [Ar] 4s 3d [Ar] half-filled stability 76

77 Periodic Table by Subshell 1s 2s 3s 2p 3p 4s 3d 4p 5s 4d 5p 6s 5d 6p 7s 6d 7p 4f 5f s block p block d block f block 1s 77

78 Verifying the Quantum Model X-Ray Photoelectron Spectroscopy (PES) X-ray ejected e - photon Energy of photon (hn) measures the energy to eject e - Why are UV and X-Ray photons used? 78

79 PES PES electron values reveal the atomic shell and subshell energies. Ne shows three PES peaks 79

80 Number of Electrons PES of Magnesium 1s 2 [Mg] = 1s 2 2s 2 2p 6 3s 2 3s 2 2p 6 2s 2 PES Photon Energy 80

81 Response to Magnetic Field Diamagnetic: all e - paired slight magnetic repulsion Paramagnetic: some e - unpaired magnetic attraction 81

82 Try It! What is e - configuration of the following elements? P Fe Pd (it is diamagnetic!) (do shorthand notation only) 82

83 Valence Electrons Electrons that are in the highest energy level are called valence electrons. These are the most important electrons when atoms bond. Why? How many valence electrons in: Na Mn Cr 83

84 Excited State Remember excited state? (e - have absorbed energy to move to a higher energy level) What atom is 1s 2 2s 2 2p 3 3s 1? 84