1. 1 ATOMIC STRUCTURE

2. 2 Chapter 7 Excited Gases & Atomic Structure

3. 3 Spectrum of White Light

4. 4 Line Emission Spectra of Excited Atoms Excited atoms emit light of only certain wavelengths The wavelengths of emitted light depend on the element.

5. 5 Spectrum of Excited Hydrogen Gas Figure 7.8

6. 6 Visible lines in H atom spectrum are called the BALMER series. High E Short Short High High Low E Long Long Low Low Line Emission Spectra of Excited Atoms

7. 7 Line Spectra of Other Elements Figure 7.9

8. 8 The Electric Pickle Excited atoms can emit light. Here the solution in a pickle is excited electrically. The Na + ions in the pickle juice give off light characteristic of that element.

9. 9 Atomic Spectra and Bohr Paradox due to the classical view: 1. Any orbit should be possible and so is any energy. 2. A charged particle moving in an electric field should emit energy. Should end up falling into the nucleus ! The classical view of atomic structure in early 20th century was that an electron (e-) traveled about the nucleus in an orbit.

10. 10 Atomic Spectra and Bohr Bohr said classical view was wrong. Needed a new theory — nowadays called OLD QUANTUM THEORY or OLD QUANTUM MECHANICS. OLD QUANTUM MECHANICS. e- can exist only in certain discrete orbits — called stationary states. e- is restricted to QUANTIZED energy states. Energy of state = - C/n 2 where n = quantum no. = 1, 2, 3, 4,....

11. 11 Atomic Spectra and Bohr Only orbits where n = integral no. are permitted.Only orbits where n = integral no. are permitted. Radius of allowed orbitals = n 2 (0.0529 nm)Radius of allowed orbitals = n 2 (0.0529 nm) But note — same eqns. come from a modern quantum mechanics approach.But note — same eqns. come from a modern quantum mechanics approach. Results can be used to explain atomic spectra.Results can be used to explain atomic spectra. Energy of quantized state = - C/n 2

12. 12 Atomic Spectra and Bohr If e-’s are in quantized energy states, then ∆E of states can have only certain values. This explain sharp line spectra.

13. 13 Atomic Spectra and Bohr Calculate ∆E for e- “falling” from a high energy level (n = 2) to a low energy level (n = 1). ∆E = E final - E initial = -C[(1/n f 2 ) - (1/n i ) 2 ], ∆E = E final - E initial = -C[(1/n f 2 ) - (1/n i ) 2 ], when n f =1 and n i =2: when n f =1 and n i =2: ∆E = -(3/4)C ∆E = -(3/4)C Note that the process is EXOTHERMIC Note that the process is EXOTHERMIC ENERGY IS EMITTED AS LIGHT ! ENERGY IS EMITTED AS LIGHT !. n = 1 n = 2 E = -C (1/2 2 ) E = -C (1/1 2 ) E N E R G Y

14. 14 ELECTROMAGNETIC RADIATION

15. 15 wavelength Visible light wavelength Ultaviolet radiation Amplitude Node Electromagnetic Radiation

16. 16 Electromagnetic Radiation Figure 7.1

17. 17 Waves have a frequencyWaves have a frequency Use the Greek letter “nu”,, for frequency, and units are “cycles per sec”Use the Greek letter “nu”,, for frequency, and units are “cycles per sec” All radiation: = cAll radiation: = c where c = velocity of light = 3.00 x 10 8 m/secwhere c = velocity of light = 3.00 x 10 8 m/sec Long wavelength --> small frequencyLong wavelength --> small frequency Short wavelength --> high frequencyShort wavelength --> high frequency Electromagnetic Radiation

18. 18 Long wavelength --> small frequency Short wavelength --> high frequency increasing frequency Electromagnetic Spectrum increasing wavelength

19. 19 Electromagnetic Radiation Red light has = 700 nm. Calculate the frequency.

20. 20 Electromagnetic Spectrum

21. 21 Atomic Spectra and Bohr ∆E = -(3/4)C C has been found from experiments (and is now called R, the Rydberg constant) R (= C) = 1312 kJ/mol or 3.29 x 10 15 cycles/sec so, E of emitted light = (3/4)R = 2.47 x 10 15 sec -1 = (3/4)R = 2.47 x 10 15 sec -1 and since = c/ = 121.6 nm This is exactly in agreement with experiment!. n = 1 n = 2 E = -C (1/2 2 ) E = -C (1/1 2 ) E N E R G Y

22. 22 Origin of Line Spectra Balmer series Figure 7.12

23. 23 Atomic Line Spectra and Niels Bohr Bohr’s theory was a great accomplishment. Rec’d Nobel Prize, 1922 Problems with theory — theory only successful for H.theory only successful for H. introduced quantum idea artificially.introduced quantum idea artificially. So, we go on toSo, we go on to MODERN QUANTUM MECHANICS or WAVE MECHANICSMODERN QUANTUM MECHANICS or WAVE MECHANICS Niels Bohr (1885-1962)

24. 24 Quantization of Energy Max Planck (1858-1947) Solved the “ultraviolet catastrophe” CCR, Figure 7.5

25. 25 E = h E = h Quantization of Energy Energy of radiation is proportional to the frequency h = Planck’s constant = 6.6262 x 10 -34 Js An object can gain or lose energy by absorbing or emitting radiant energy in QUANTA.

26. 26 Photoelectric Effect Experiment demonstrates the particle nature of light.

27. 27 Photoelectric Photoelectric Effect Classical theory said that E of ejected electron should increase with increase in light intensity—not observed! No e - observed until light of a certain minimum E is used.No e - observed until light of a certain minimum E is used. Number of e - ejected depends on light intensity.Number of e - ejected depends on light intensity. A. Einstein (1879-1955)

28. 28 PROBLEM: Calculate the energy of 1.00 mol of photons of red light. = 700. nm = 700. nm = 4.29 x 10 14 sec -1 = 4.29 x 10 14 sec -1 PROBLEM: Calculate the energy of 1.00 mol of photons of red light. = 700. nm = 700. nm = 4.29 x 10 14 sec -1 = 4.29 x 10 14 sec -1 Photoelectric Effect Understand experimental observations if light consists of particles called PHOTONS of discrete energy.

29. 29 Energy of Radiation Energy of 1.00 mol of photons of red light. E = h E = h = (6.63 x 10 -34 Js)(4.29 x 10 14 sec -1 ) = (6.63 x 10 -34 Js)(4.29 x 10 14 sec -1 ) = 2.85 x 10 -19 J per photon = 2.85 x 10 -19 J per photon E per mol = (2.85 x 10 -19 J/ph)(6.02 x 10 23 ph/mol) (2.85 x 10 -19 J/ph)(6.02 x 10 23 ph/mol) = 171.6 kJ/mol = 171.6 kJ/mol This is in the range of energies that can break bonds.

30. 30 Quantum or Wave Mechanics de Broglie (1924) proposed that all moving objects have wave properties (mass)(velocity) = h / (mass)(velocity) = h / Note that this relation also applies to electromagnetic radiation: mc = h /  or h = mc  mc = h /  or h = mc  and since E = h and = c /   E = mc 2  which is Einstein’s famous equation for the relation between mass and energy de Broglie (1924) proposed that all moving objects have wave properties (mass)(velocity) = h / (mass)(velocity) = h / Note that this relation also applies to electromagnetic radiation: mc = h /  or h = mc  mc = h /  or h = mc  and since E = h and = c /   E = mc 2  which is Einstein’s famous equation for the relation between mass and energy L. de Broglie (1892-1987)

31. 31 Baseball (115 g) at 100 mph = 1.3 x 10 -32 cm = 1.3 x 10 -32 cm e- with velocity = 1.9 x 10 8 cm/sec = 0.388 nm = 0.388 nm Experimental proof of wave properties of electrons Quantum or Wave Mechanics

32. 32 Schrödinger applied the idea of e- behaving as a wave to the problem of electrons in atoms. He developed the WAVE EQUATION: H  whose solution gives the so-called WAVE FUNCTION,  Describing an allowed state  of energy state E Quantization introduced naturally. E. Schrodinger 1887-1961 Quantum or Wave Mechanics

33. 33 WAVE FUNCTIONS,   x  is a function of coordinates, x.  x  is a function of coordinates, x. Each  corresponds to an ORBITAL — the region of space within which an electron is found. Each  corresponds to an ORBITAL — the region of space within which an electron is found.  does NOT describe the exact location of the electron.  does NOT describe the exact location of the electron.  2 is proportional to the probability of finding an e- at a given point.  2 is proportional to the probability of finding an e- at a given point.

34. 34 Uncertainty Principle Problem of defining nature of electrons in atoms solved by W. Heisenberg. Cannot simultaneously define the position and momentum (p= mv) of an electron:  x  p  h/(2  ) If we determine the e- velocity, precisely we can not determine the position very well and viceversa. Problem of defining nature of electrons in atoms solved by W. Heisenberg. Cannot simultaneously define the position and momentum (p= mv) of an electron:  x  p  h/(2  ) If we determine the e- velocity, precisely we can not determine the position very well and viceversa. W. Heisenberg 1901-1976

35. 35 Types of Orbitals s orbital p orbital d orbital

36. 36 Orbitals No more than 2 e- assigned to an orbitalNo more than 2 e- assigned to an orbital Orbitals grouped in s, p, d (and f) subshellsOrbitals grouped in s, p, d (and f) subshells s orbitals d orbitals p orbitals

37. 37 s orbitals d orbitals p orbitals s orbitals p orbitals d orbitals No.orbs. No. e- 135 2610

38. 38 Subshells & Shells Each shell has a number called the PRINCIPAL QUANTUM NUMBER, nEach shell has a number called the PRINCIPAL QUANTUM NUMBER, n The principal quantum number of the shell is the number of the period or row of the periodic table where that shell begins.The principal quantum number of the shell is the number of the period or row of the periodic table where that shell begins.

39. 39 Subshells & Shells n = 1 n = 2 n = 3 n = 4

40. 40 QUANTUM NUMBERS The shape, size, and energy of each orbital is a function of 3 quantum numbers: n (major) ---> shell l (angular) ---> subshell m l (magnetic) ---> designates an orbital within a subshell

41. 41 SymbolValuesDescription n (major)1, 2, 3,... Orbital size, energy, and # of nodes=n-1 l (angular)0, 1, 2,... n-1 Orbital shape or type (subshell) m l (magnetic)-l,...0,...+l Orbital orientation # of orbitals in subshell = 2 l + 1 # of orbitals in subshell = 2 l + 1 QUANTUM NUMBERS

42. 42 Types of Atomic Orbitals

43. 43 Shells and Subshells When n = 1, then l = 0 and m l = 0 Therefore, in n = 1, there is 1 type of subshell and that subshell has a single orbital (m l =0 has a single value ---> 1 orbital) This subshell is labeled s (“ess”) Each shell has 1 orbital labeled s, and it is SPHERICAL in shape.

44. 44 s Orbitals See Figure 7.14 on page 274 and Screen 7.13. All s orbitals are spherical in shape.

45. 45 1s Orbital

46. 46 2s Orbital

47. 47 3s Orbital

48. 48 p Orbitals When n = 2, then l = 0 and l = 1 Therefore, when n = 2 there are 2 types of orbitals — 2 subshells For l = 0m l = 0, s subshell For l = 1 m l = -1, 0, +1 this is a p subshell with 3 orbitals this is a p subshell with 3 orbitals When n = 2, then l = 0 and l = 1 Therefore, when n = 2 there are 2 types of orbitals — 2 subshells For l = 0m l = 0, s subshell For l = 1 m l = -1, 0, +1 this is a p subshell with 3 orbitals this is a p subshell with 3 orbitals See Screen 7.13 When l = 1, there is a NODAL PLANE

49. 49 p Orbitals The three p orbitals are oriented 90 o apart in spaceThe three p orbitals are oriented 90 o apart in space

50. 50 2p x Orbital 3p x Orbital

51. 51 d Orbitals When n = 3, what are the values of l? l = 0, 1, 2 and so there are 3 subshells in the shell. For l = 0, m l = 0 ---> s subshell with single orbital ---> s subshell with single orbital For l = 1, m l = -1, 0, +1 ---> p subshell with 3 orbitals ---> p subshell with 3 orbitals For l = 2, m l = -2, -1, 0, +1, +2 ---> d subshell with 5 orbitals ---> d subshell with 5 orbitals

52. 52 d Orbitals s orbitals have no planar node (l = 0) and so are spherical. p orbitals have l = 1, and have 1 planar node, and so are “dumbbell” shaped. This means d orbitals (with l = 2) have 2 planar nodes See Figure 7.16

53. 53 3d xy Orbital

54. 54 3d xz Orbital

55. 55 3d yz Orbital

56. 56 3d x 2 - y 2 Orbital

57. 57 3d z 2 Orbital