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

2. Properties of Waves Wavelength ( ): distance between identical points on successive waves. Amplitude: vertical distance from the midline of a wave to the peak or trough (brightness and intensity)

3. Properties of Waves Frequency ( ): number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s). The speed of the wave = x

4. Maxwell (1873): visible light consists of electromagnetic waves. Speed of light (c) in vacuum = 3.00 x 10 8 m/s All electromagnetic radiation x  c

5. Electromagnetic Spectrum Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves.

6. x = c = c/ = 3.00 x 10 8 m/s / 6.0 x 10 4 Hz = 5.0 x 10 3 m Radio wave A photon has a frequency of 6.0 x 10 4 Hz. Convert this frequency into wavelength (nm). Does this frequency fall in the visible region? = 5.0 x 10 12 nm

7. “Black Body 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

8. Light has both: 1.wave nature 2.particle nature h = KE + BE “Photoelectric Effect” Solved by Einstein in 1905 Photon is a “particle” of light KE = h - BE h KE e - photoelectric effect: the emission of electrons from a metal when light shines on the metal

9. E = h x E = 6.63 x 10 -34 (J s) x 3.00 x 10 8 (m/s) / 0.154 x 10 -9 (m) E = 1.29 x 10 -15 J E = h x c /  When copper is bombarded with high-energy electrons, X rays are emitted. Calculate the energy (in joules) associated with the photons if the wavelength of the X rays is 0.154 nm.

10. Definitions Ground State: – ALL electrons are in the lowest possible energy levels Excited State: – Electrons absorb energy and are boosted to a higher energy level Emission: – when an electron falls to a lower energy level, a photon is emitted Absorption: – energy must be added to an atom in order to move an electron from a lower energy level to a higher energy level

11. 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

12. Line Spectrum Every element has a different number of electrons. Every element will have different transitions of electrons between energy levels. Each element has their own unique line spectrum created from the release of photons of light. When are photons released?

13. Line Emission Spectrum of Hydrogen Atoms

15. E = h Electrons can only move with a quantum of energy. Every color represents a different amount of energy released.

16. 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

17. E photon = 2.18 x 10 -18 J x (1/25 - 1/9) E photon =  E = -1.55 x 10 -19 J = 6.63 x 10 -34 (Js) x 3.00 x 10 8 (m/s)/1.55 x 10 -19 J = 1280 nm Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 3 state. E photon = h x c /  = h x c / E photon i f  E = R H ( ) 1 n2n2 1 n2n2 E photon =

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

19. = h/mu = 6.63 x 10 -34 / (2.5 x 10 -3 x 15.6) = 1.7 x 10 -32 m = 1.7 x 10 -23 nm What is the de Broglie wavelength (in nm) associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s? m in kgh in J su in (m/s)

20. Heisenberg Uncertainty Principle Electrons have a dual nature: – If it is a wave, then we know how fast it is moving – If it is a particle; then, we know its position. WE CANNOT KNOW AN ELECTRONS EXACT POSITION OR SPEED AT THE SAME TIME

21. Schrodinger Wave Equation equation that describes both the particle and wave nature of the e - The equation is called a wave function (  ) it describes: 1. energy of e - with a given  2. 90% 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.

22. e - density (1s orbital) falls off rapidly as distance from nucleus increases Where 90% of the e - density is found for the 1s orbital

23. We do not know the exact location of an electron, but we do our best to DESCRIBE it’s location.

24. DO NOW 1. Take out homework. 2. Pick up four colors from the bin up front. 3. Answer the questions below. How would you describe your current location? Start off really broad, as in the United States, and describe your location to be more specific. How would you describe the location of an electron? Do electrons stay in the same place?

25. The first four principle energy levels in the atom.

26. ENERGY LEVEL SUB- LEVEL

27. The first four principle energy levels and their sub-levels.

30. SUB- LEVEL ORBITAL

31. The first four principle energy levels, their sub-levels, and orbitals. Energy 1s 2s 3s 4s 5s 2p 3p 4p 3d 4d 4f

32. Aufbau Principle 4s 5s 1s 2s 3s 2p 3p 4p 3d 4d Energy 4f Electrons are added one at a time Starting at the lowest available Energy orbital. Electron Configuration for: Boron

33. m s = +½ or -½ How many electrons can an orbital hold? An orbital can hold 2 electrons

34. Pauli Exclusion Principle 1s 2s 3s 4s 5s 2p 3p 4p 3d 4d Energy 4f Can not have same set of Quantum Numbers An orbital holds a max of 2 electrons. Must have opposite spins. - Paired electrons - Unpaired electron Electron Configuration for: Boron

35. Hund’s Rule 1s 2s 3s 4s 5s 2p 3p 4p 3d 4d Energy 4f Electrons occupy equal energy orbitals So that a maximum number of unpaired Electrons results. Electron Configuration for: Oxygen

36. What is the electron configuration of Mg? Mg 12 electrons 2 + 2 + 6 + 2 = 12 electrons Energy 1s 2s 3s 4s 5s 2p 3p 4p 3d 4d

37. What is the electron configuration of Cl? Cl 17 electrons 2 + 2 + 6 + 2 + 5 = 17 electrons 1s 2s 3s 4s 5s 2p 3p 4p 3d 4d Energy

38. Exceptions Chromium Copper

39. Quantum Numbers

40. Schrodinger Wave Equation  fn(n, l, m l, m s ) principal quantum number n n = 1, 2, 3, 4, …. n=1 n=2 n=3 distance of e - from the nucleus

41.  = fn(n, l, m l, m s ) angular momentum quantum number l for a given value of n, l = 0, 1, 2, 3, … n-1 n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 Shape of the “volume” of space that the e - occupies l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital Schrodinger Wave Equation

42. l = 0 (s orbitals) l = 1 (p orbitals)

43. l = 2 (d orbitals)

44.  = fn(n, l, m l, m s ) magnetic quantum number m l for a given value of l m l = -l, …., 0, …. +l orientation of the orbital in space if l = 1 (p orbital), m l = -1, 0, or 1 if l = 2 (d orbital), m l = -2, -1, 0, 1, or 2 Schrodinger Wave Equation

45. m l = -1m l = 0m l = 1 m l = -2m l = -1m l = 0m l = 1m l = 2

46.  = fn(n, l, m l, m s ) spin quantum number m s m s = +½ or -½ Schrodinger Wave Equation m s = -½m s = +½

47. How many 2p orbitals are there in an atom? 2p n=2 l = 1 If l = 1, then m l = -1, 0, or +1 3 orbitals How many electrons can be placed in the 3d subshell? 3d n=3 l = 2 If l = 2, then m l = -2, -1, 0, +1, or +2 5 orbitals which can hold a total of 10 e -

48. 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

49. 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

50. What is the electron configuration of Mg? Mg 12 electrons 1s < 2s < 2p < 3s < 3p < 4s 1s 2 2s 2 2p 6 3s 2 2 + 2 + 6 + 2 = 12 electrons Abbreviated as [Ne]3s 2 [Ne] 1s 2 2s 2 2p 6 What are the possible quantum numbers for the last (outermost) electron in Cl? Cl 17 electrons1s < 2s < 2p < 3s < 3p < 4s 1s 2 2s 2 2p 6 3s 2 3p 5 2 + 2 + 6 + 2 + 5 = 17 electrons Last electron added to 3p orbital n = 3l = 1m l = -1, 0, or +1m s = ½ or -½

51. Outermost subshell being filled with electrons

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