1. Chapter 7 The Quantum Mechanical Model of the Atom

2. Quantum mechanics — microscopic particles Classical mechanics — macroscopic objects

3. Some properties of light

4. Light travels and carries energy

5. Speed of light c = 3.00 x 10 8 m/s

6. Light has many colors

7. Light can be invisible to human

9. Light is an electromagnetic radiation Light is a wave

10. Wavelength λ: distance between two consecutive peaks. Unit: m

12. Frequency ν : number of complete wavelengths, or cycles, that pass a given point each second. Unit: 1/s = s −1 = Hz Period T: time required for a complete wavelength or cycle to pass a given point. Unit: s ν = 1/T c = λ/T = λ ν

13. Demo on Sr salt λ = 6.50 x 10 2 nm, what is the frequency of the red light? What is the period of the light?

14. ν

16. 1. Blackbody radiation Phenomena that could not be explained by classic mechanics

17. ρ(λ) (kJ/nm)

18. Energy can only be gained or lost in whole-number multiples of the quantity h v, a quantum. Planck’s constant: h = 6.63 x 10 −34 J·s

21. 1. Blackbody radiation Phenomena that could not be explained by classic mechanics 2. Photoelectric effect

22. Photoelectric Effect Occurs only if ν > ν 0

23. Electromagnetic radiation can be viewed as a stream of particles called photons. Energy of one photon is E = h ν

25. What is the energy of one photon from the red light? What is the energy of one photon from a yellow light whose wavelength is 589 nm? 3.37 x 10 −19 J 3.06 x 10 −19 J4.61 x 10 14 Hz 5.09 x 10 14 Hz

26. ν

27. Electromagnetic Radiation Exhibits Wave Properties and Particulate Properties Is light a stream of particles or waves?

29. 1. Blackbody radiation Phenomena that could not be explained by classic mechanics 2. Photoelectric effect 3. Atomic spectra

30. Pink Floyd: Dark Side of the Moon

31. λ Continuous spectrum

32. Ne gas in tube

34. HgHeH

36. Electrons in an atom can only occupy certain energy levels Neils Bohr

40. Unknown volatile liquid: methanol CH 3 OH

41. Schrödinger’s Equation Ĥ — an operator related to energy E — energy Ψ — wave function Ψ contains all the information of a system Ψ = Ψ(x,y,z) x,y,z: coordinates of electrons

42. H atom

43. │Ψ(x,y,z)│ 2 — probability density distribution of electrons Max Born Ψ — wave function Ψ contains all the information of a system What is the physical significance of Ψ?

45. A specific wave function Ψ is called an orbital. An atomic orbital is characterized by three quantum numbers.

46. Three Quantum Numbers Principle quantum number n. Only positive integers. n = 1, 2, 3, 4, · · ·shell Angular momentum quantum number l. l = 0, 1, 2, 3, 4, · · ·, (n − 1)subshell s p d f g

47. Magnetic quantum number m l m l = − l, − l +1, − l + 2, · · ·, 0, · · ·, l − 1, l Must remember the possible values for quantum numbers One set of n, l, and m l specify One atomic orbital.

48. The sets of quantum numbers are each supposed to specify an orbital. One set, however, is erroneous. Which one and why? (a) n = 3; l = 0; m l = 0(b) n = 2; l = 1; m l = – 1 (c) n = 1; l = 0; m l = 0(d) n = 4; l = 1; m l = – 2 EXAMPLE 7.6 Quantum Numbers II n = 1, 2, 3, 4, · · · l = 0, 1, 2, 3, 4, · · ·, (n − 1) m l = − l, − l +1, − l + 2, · · ·, 0, · · ·, l − 1, l

49. Which of the following names are incorrect: 1s, 1p, 7d, 9s, 3f, 4f, 2d n = 1, 2, 3, 4, · · · l = 0, 1, 2, 3, 4, · · ·, (n − 1) m l = − l, − l +1, − l + 2, · · ·, 0, · · ·, l − 1, l

50. What are the quantum numbers and names (for example, 2s, 2p) of the orbitals in the n = 4 principal level? How many n = 4 orbitals exist? n = 1, 2, 3, 4, · · · l = 0, 1, 2, 3, 4, · · ·, (n − 1) m l = − l, − l +1, − l + 2, · · ·, 0, · · ·, l − 1, l n = 4; therefore l = 0, 1, 2, and 3

51. Try “For practice 7.5 and 7.6” on page 299 and homework questions

52. 1s orbital of H atom How to represent an orbital in 3D? 2) Contour surface 1) Probability distribution

54. 1s orbital of H atom How to represent an orbital in 3D? 2) Contour surface 90 % 1) Probability distribution

56. Two Representations of the Hydrogen 1s, 2s, and 3s Orbitals (a) The Electron Probability Distribution (b) The Surface Contains 90% of the Total Electron Probability (the Size of the Oribital, by Definition) n↑ → size↑

57. Representation of the 2p Orbitals (a) The Electron Probability Distribution for a 2p Oribtal (b) The Boundary Surface Representations of all Three 2p Orbitals l is related to shape of orbitals

58. Representation of the 3d Orbitals (a) Electron Density Plots of Selected 3d Orbitals (b) The Boundary Surfaces of All of the 3d Orbitals

60. Chapter 7 Problems 5, 20, 28, 32, 59, 61, 63