1. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Chapter 7 (Zumdahl) Electronic Structure of Atoms Chemistry, The Central Science, 11th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten John D. Bookstaver St. Charles Community College Cottleville, MO

2. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Waves To understand the electronic structure of atoms, one must understand the nature of electromagnetic (EM) radiation. The distance between corresponding points on adjacent waves is the wavelength ( ).

3. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Waves The number of waves passing a given point per unit of time is the frequency ( ). For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency. Frequency is measured in the following units: s -1, = waves/s = Hz (hertz)

4. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Electromagnetic Radiation All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00  10 8 m/s. Therefore, c =

5. Electronic Structure of Atoms Sample Exercise 7.1 (p 292) (Copy from text into notes.) Follow as I review the book solution to this problem. © 2009, Prentice-Hall, Inc.

6. Electronic Structure of Atoms #39: The laser in an audio compact disc player uses light with a wavelength of 7.80 x 10 2 nm. Calculate the frequency of this light. Solution: label your given(s) & your unknown.  = given = unknown Identify the connection between given(s) and unknown. (c= ) Recognize that you know the value of c for all EM radiation ( c =3.00 x 10 8 m/s) Substitute in all given/known values & solve for the unknown. (NOTE: Convert nm to m first!) © 2009, Prentice-Hall, Inc. Practice Problems: Text, p 337,#39-40

7. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy The wave nature of light does not explain how an object can glow when its temperature increases. Max Planck explained it by assuming that energy comes in packets called quanta.

8. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy Einstein used this assumption to explain the photoelectric effect. He concluded that energy is proportional to frequency: E = h where h is Planck’s constant, 6.626  10 −34 J-s. He also concluded that wave energy has mass!

9. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light (also known as a “quantum” of energy): c = E = h

10. Electronic Structure of Atoms Sample Exercise 7.2 p 293-294 Copy this problem and solution. Follow along as we walk thru the solution together. The blue color in fireworks is often achieved by heating copper(I) chloride (CuCl) to about 1200 C. Then the compound emits blue light having a wavelength of 450 nm. What is the increment of energy (the quantum) that is emitted by CuCl? © 2009, Prentice-Hall, Inc.

11. Electronic Structure of Atoms Solution: label your given(s) & your unknown.  = givenE= unknown Identify the connection between given(s) and unknown. –There is not a direct connection. No equation we have includes both E and  –However, we know that E = h –We also know the value of h (=6.626 x 10 −34 J-s). –If we know the value of, we can calculate E. Can we find ? (is there a connection between and ? –YES! c=. Substitute given values into this second equation and solve for. (Don’t forget to convert from nm to m first!) When is obtained, substitute it and the value of h into the first equation and solve for E. © 2009, Prentice-Hall, Inc.

12. Electronic Structure of Atoms Practice Problems p 337, #41-44 © 2009, Prentice-Hall, Inc.

13. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy Another mystery in the early 20th century involved the emission spectra observed from energy emitted by atoms and molecules.

14. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy For atoms and molecules one does not observe a continuous spectrum, as one gets from a white light source. Only a line spectrum of discrete wavelengths is observed.

15. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: 1.Electrons in an atom can only occupy certain orbits (corresponding to certain energies).

16. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: 2.Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.

17. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: 3.Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by E = nh Where n=main energy level

18. Electronic Structure of Atoms Solving for e- energy if & are unknown The energy of an electron in a hydrogen atom is E= (-2.178 x 10 -18 J) Z 2 n 2 © 2009, Prentice-Hall, Inc. [] Where Z= nuclear charge (atomic #) and n = main energy level and R H = the Rydberg constant, 2.18  10 −18 J

19. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation:  E = −R H ( ) 12nf212nf2 12ni212ni2 - n i and n f are the initial and final energy levels of the electron. And Z = 1 (atomic # of hydrogen!)

20. Electronic Structure of Atoms Sample Exercise P 338 #51a. Calculate the energy emitted when the following transition occurs in a hydrogen atom: n=3  n= 2 © 2009, Prentice-Hall, Inc.

21. Electronic Structure of Atoms Solution Our givens are –n final (level 2) –n initial (level 3) Our unknown is the energy released (  E) Identify the connection between given(s) & unknown:  E= -R H (1/n f 2 -1/n i 2 ) Substitute given values & solve for unknown! © 2009, Prentice-Hall, Inc.

22. Electronic Structure of Atoms Calculating  of light from energy released Continue w/#51 from p 338 Calculate the wavelength of light emitted when the following transition occurs in the hydrogen atom. What type of EM radiation is emitted? Givens:  E (from prior slide) Unknown: Connection: E = h  to solve for then use c=  to solve for  Substitute & Solve: © 2009, Prentice-Hall, Inc.

23. Electronic Structure of Atoms ALTERNATIVE APPROACH Derive formula that includes all the variables you are using:  E Use both eqns E = h c=  1.Set both eqns equal to –E = c=  h 2.Set both eqns equal to one another –E =c h 3.Isolate  since this is your unknown.  = hc E 4. Substitute values (c, h, E) to solve for  © 2009, Prentice-Hall, Inc.

24. Electronic Structure of Atoms Practice Problems: p 338, #51, 52, 53, 54, 55, 56 © 2009, Prentice-Hall, Inc.

25. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Wave Nature of Matter Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties. He demonstrated that the relationship between mass and wavelength was = h mv Please note: the base units for Joules are kg●m 2 /s 2. This will be important for calculations This formula is on the AP exam formula sheet

26. Electronic Structure of Atoms Wave-Particle Duality Site with Cool Visuals & Explanation of Wave Interference, Including electron wavesSite with Cool Visuals © 2009, Prentice-Hall, Inc.

27. Electronic Structure of Atoms Sample Exercise (from Brown/Lemay) p 223 What is the wavelength of an electron moving with a speed of 5.97 x 10 6 m/s? The mass of the electron is 9.11 x 10 -31 kg. SOLUTION: Givens: m electron = 9.11 x 10 -31 kg v electron = 5.97 x 10 6 m/s Unknown = CONNECTION between givens & unknown:  h mv Substitute given & constant values, solve for  © 2009, Prentice-Hall, Inc.

28. Electronic Structure of Atoms Sample Exercise, cont. Substitute given & constant values, solve for   h mv  6.626 x 10 -34 kg●m 2 /s (9.11 x 10 -31 kg)(5.97 x 10 6 m/s)  1.22 x 10 -10 © 2009, Prentice-Hall, Inc. J= kg●m 2 /s 2 Where did the exponent go?

29. Electronic Structure of Atoms Practice Problems 6.41) Determine the wavelength of the following objects a)An 85-kg person skiing at 50 km/hr b)A 10.0 g bullet fired at 250 m/s. c)A lithium atom moing at 2.5 x 10 5 m d)An ozone molecule in the upper atmosphere moving at 550 m/s. © 2009, Prentice-Hall, Inc.

30. Electronic Structure of Atoms Practice Problems: 6.42) Among the elementary subatomic particles of physics is the muon, which decays within a few nanoseconds after formation. The muon has a mass 206.8 times that of an electron. Calculate the deBroglie wavelength associated with a muon traveling at 8.85 x 10 5 cm/s. © 2009, Prentice-Hall, Inc.

31. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Uncertainty Principle Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known: In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself! (  x) (  mv)  h4h4

32. Electronic Structure of Atoms Sample Exercise P 338, # 59 Using Heisenberg uncertainty principle, calculate ∆x for each of the following: a) electron with a v = 0.100 m/s © 2009, Prentice-Hall, Inc.

33. Electronic Structure of Atoms Practice Problems Complete p 338 #59 & 60 © 2009, Prentice-Hall, Inc.

34. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Quantum Mechanics Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. It is known as quantum mechanics.

35. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Quantum Mechanics The wave equation is designated with a lower case Greek psi (  ). The square of the wave equation,  2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.

36. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Quantum Numbers Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. Each orbital describes a spatial distribution of electron density. An orbital is described by a set of three quantum numbers.

37. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Principal Quantum Number (n) The principal quantum number, n, describes the energy level on which the orbital resides. The values of n are integers ≥ 1.

38. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Angular Momentum Quantum Number (l) This quantum number defines the shape of the orbital. Allowed values of l are integers ranging from 0 to n − 1. We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.

39. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Angular Momentum Quantum Number (l) Value of l0123 Type of orbitalspdf

40. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Magnetic Quantum Number (m l ) The magnetic quantum number describes the three-dimensional orientation of the orbital. Allowed values of m l are integers ranging from -l to l: −l ≤ m l ≤ l. Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.

41. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Magnetic Quantum Number (m l ) Orbitals with the same value of n form a shell. Different orbital types within a shell are subshells.

42. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. s Orbitals The value of l for s orbitals is 0. They are spherical in shape. The radius of the sphere increases with the value of n.

43. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. s Orbitals Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron.

44. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. p Orbitals The value of l for p orbitals is 1. They have two lobes with a node between them.

45. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. d Orbitals The value of l for a d orbital is 2. Four of the five d orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.

46. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Energies of Orbitals For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. That is, they are degenerate.

47. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Energies of Orbitals As the number of electrons increases, though, so does the repulsion between them. Therefore, in many- electron atoms, orbitals on the same energy level are no longer degenerate.

48. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Spin Quantum Number, m s In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy. The “spin” of an electron describes its magnetic field, which affects its energy.

49. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Spin Quantum Number, m s This led to a fourth quantum number, the spin quantum number, m s. The spin quantum number has only 2 allowed values: +1/2 and −1/2.

50. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Pauli Exclusion Principle No two electrons in the same atom can have exactly the same energy. Therefore, no two electrons in the same atom can have identical sets of quantum numbers.

51. Electronic Structure of Atoms Sample Exercise: 7.6 p 308 © 2009, Prentice-Hall, Inc.

52. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Electron Configurations This shows the distribution of all electrons in an atom. Each component consists of –A number denoting the energy level,

53. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Electron Configurations This shows the distribution of all electrons in an atom Each component consists of –A number denoting the energy level, –A letter denoting the type of orbital,

54. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Electron Configurations This shows the distribution of all electrons in an atom. Each component consists of –A number denoting the energy level, –A letter denoting the type of orbital, –A superscript denoting the number of electrons in those orbitals.

55. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Orbital Diagrams Each box in the diagram represents one orbital. Half-arrows represent the electrons. The direction of the arrow represents the relative spin of the electron.

56. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Hund’s Rule “For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.” Another translation: “Don’t pair electrons in degenerate orbitals until there is 1 electron in each orbital.”

57. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Periodic Table We fill orbitals in increasing order of energy. Different blocks on the periodic table (shaded in different colors in this chart) correspond to different types of orbitals.

58. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Some Anomalies Some irregularities occur when there are enough electrons to half- fill s and d orbitals on a given row.

59. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Some Anomalies For instance, the electron configuration for copper is [Ar] 4s 1 3d 5 rather than the expected [Ar] 4s 2 3d 4.

60. Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Some Anomalies This occurs because the 4s and 3d orbitals are very close in energy. These anomalies occur in f-block atoms, as well.