1. 1 Chapter 7 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Quantum Theory and the Electronic Structure of Atoms

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3. 3 Properties of Waves Wavelength ( ) is the distance between identical points on successive waves. Amplitude is the vertical distance from the midline of a wave to the peak or trough. Frequency ( ) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s). The speed (u) of the wave = x

4. Review of Concept Which of the waves shown has (a) the highest frequency (b) the longest wavelength (c) the greatest amplitude? 4

5. 5 Maxwell (1873), proposed that visible light consists of electromagnetic waves. Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves. Speed of light (c) in vacuum = 3.00 x 10 8 m/s All electromagnetic radiation x  c

6. Example 7.1 The wavelength of the green light from a traffic signal is centered at 522 nm. What is the frequency of this radiation? Pg 279

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8. 8 Mystery #1, “Heated Solids Problem” Solved by Planck in 1900 Energy (light) is emitted or absorbed in discrete units (quantum). E = h x Planck’s constant (h) h = 6.63 x 10 -34 J s When solids are heated, they emit electromagnetic radiation over a wide range of wavelengths. Radiant energy emitted by an object at a certain temperature depends on its wavelength. E = hc / λ Because  = c/λ h = 6.63 x 10 -34 J s

9. Review of Concept Why is radiation only in the UV but not the visible or infrared region responsible for sun tanning? 9

10. Example 7.2 Calculate the energy (in joules) of (a) a photon with a wavelength of 5.00 × 10 4 nm (infrared region) (b) a photon with a wavelength of 5.00 × 10 −2 nm (X ray region) Pg 282

11. 11 Light has both: 1.wave nature 2.particle nature Mystery #2, “Photoelectric Effect” Solved by Einstein in 1905 Photoelectric effect phenomenon in which electrons are ejected from the surface of certain metals exposed to light of at least a certain minimum frequency (threshold frequency) Photon is a “particle” of light h KE e -

12. Bohr’s Theory of the Hydrogen atom 12

13. 13 Line Emission Spectrum of Hydrogen Atoms Energize the sample

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15. 15 1.e - can only have specific (quantized) energy values 2.light is emitted as e - moves from one energy level to a lower energy level Bohr’s Model of the Atom (1913) E n = −R H ( ) 1 n2n2 n (principal quantum number) = 1,2,3,… R H (Rydberg constant) = 2.18 x 10 -18 J

16. 16 E = h

17. 17 E photon =  E = E f - E i E f = -R H ( ) 1 n2n2 f E i = -R H ( ) 1 n2n2 i i f  E = R H ( ) 1 n2n2 1 n2n2 n f = 1 n i = 2 n f = 1 n i = 3 n f = 2 n i = 3

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19. Example 7.4 What is the wavelength of a photon (in nanometers) emitted during a transition from the n i = 5 state to the n f = 2 state in the hydrogen atom? Pg 288

20. THE DUEL NATURE OF THE ELECTRON 20

21. Standing Waves 21

22. 22 De Broglie (1924) reasoned that e - is both particle and wave. Why is e - energy quantized? v = velocity of e- m = mass of e- 2  r = n = h mv

23. Example 7.5 Pg 292

24. QUANTUM MECHANICS 24

25. Heisenberg Uncertainty principle 25 Δx Δp ≥ h 4π

26. 26 Schrodinger Wave Equation In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e - Wave function (  ) describes: 1. energy of e - with a given  2. probability of finding e - in a volume of space   Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems.

27. QUANTUM NUMBERS 27

28. 28 n = 1, 2, 3, 4, …. n=1 n=2 n=3 distance of e - from the nucleus principal quantum number n

29. 29 Shape of the “volume” of space that the e - occupies Sublevels: s orbital p orbital d orbital f orbital Sublevels

30. s orbital (1 orientation: sphere)

31. p orbital (3 orientations: dumbbells)

32. d orbital (5 orientations: double dumbbells)

33. f orbital (7 orientations)

34. 34 Spin

35. 35 Energy of orbitals in a single electron atom Energy only depends on principal quantum number n E n = -R H ( ) 1 n2n2 n=1 n=2 n=3

36. 36 Energy of orbitals in a multi-electron atom Energy depends on n and l n=1 l = 0 n=2 l = 0 n=2 l = 1 n=3 l = 0 n=3 l = 1 n=3 l = 2

37. 37 Electron configuration is how the electrons are distributed among the various atomic orbitals in an atom. 1s 1 principal quantum number n Sublevel (shape) number of electrons in the orbital Orbital diagram H 1s 1

38. 38 “Fill up” electrons in lowest energy orbitals (Aufbau principle)

39. 39 Pauli exclusion principle - no two electrons in an atom can have the same four quantum numbers. Each seat is uniquely identified (E, R12, S8). Each seat can hold only one individual at a time.

40. 40 Paramagnetic unpaired electrons 2p Diamagnetic all electrons paired 2p

41. Shielding Effect 41 Why is the 2s orbital lower in energy than the 2p? “shielding” reduces the electrostatic attraction Energy difference also depends on orbital shape

42. 42 The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule).

43. 43 Order of orbitals (filling) in multi-electron atom 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

44. 44 Outermost subshell being filled with electrons

45. Example 7.11 An oxygen atom has a total of eight electrons. Write the ground state electron configuration and orbital diagram. Pg 309

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47. Noble Gas Configuration Ex: Aluminum e − configuration: 1s 2 2s 2 2p 6 3s 2 3p 1 preceding noble gas is Ne: 1s 2 2s 2 2p 6 noble gas configuration: [Ne] 3s 2 3p 1 47

48. Example Write the noble gas configuration and the noble gas orbital diagram for sulfur (S).

49. Example 7.12 Because palladium is diamagnetic, all the electrons are paired and its electron configuration must be 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 4d 10 or simply [Kr]4d 10. The configurations in (2) and (3) both represent paramagnetic elements. Check To confirm the answer, write the orbital diagrams for (1), (2), and (3).