1. Quantum Physics Eleanor Roosevelt High School Chin-Sung Lin Lesson 27

2. The Model of Atom

3. The Planetary Model of Atom Niels Bohr’s model Positive charge is in the center of the atom (nucleus ) Atom has zero net charge Electrons orbit the nucleus like planets orbit the sun Attractive Coulomb force plays role of gravity

4. The Planetary Model of Atom Circular motion of orbiting electrons causes them to emit electromagnetic radiation with frequency equal to orbital frequency, and carries away energy from the electron –Electron predicted to continually lose energy –The electron would eventually spiral into the nucleus However most atoms are stable!

5. The Planetary Model of Atom Experimentally, atoms do emit electromagnetic radiation, but not just any radiation! Each atom has its own ‘fingerprint’ of different light frequencies that it emits Hydrogen Mercury Wavelength (nm) 400 nm 500 nm 600 nm700 nm

6. The Planetary Model of Atom n = 3, = 656.3 nm Hydrogen n = 4, = 486.1 nm n=3n=4 The Balmer Series of emission lines empirically given by

7. One electron orbits around one proton and only certain orbits are stable Radiation emitted only when electron jumps from one stable orbit to another Here, the emitted photon has an energy of E initial – E final E initial E final Photon The Planetary Model of Atom

8. Hydrogen emits only photons of a particular wavelength, frequency Photon energy = hf, so this means a particular energy The Planetary Model of Atom

9. Energy is quantized Zero energy n=1 n=2 n=3 n=4 Energy axis The Planetary Model of Atom

10. Photon is emitted when electron drops from one quantum state to another Zero energy n=1 n=2 n=3 n=4 n=1 n=2 n=3 n=4 Absorbing a photon of correct energy makes electron jump to higher quantum state. Photon absorbed hf=E 2 -E 1 Photon emitted hf=E 2 -E 1 The Planetary Model of Atom

11. A useful model of the atom must be consistent with a model for light, for most of what we know about atoms we learn from the light and other radiations they emit Most light has its source in the motion of electrons within the atom

12. Models of Light

13. The Model of Light Two primary models of light: the particle model and the wave model

14. The Model of Light Isaac Newton believed in a particle model of light Christian Huygens believed that light was a wave Thomas Young demonstrated the wave property of light – Interference James Clerk Maxwell proposed that light is a part of broader electromagnetic wave spectrum Heinrich Hertz produced radio wave as Maxwell’s prediction Albert Einstein resurrected the particle theory of light

15. Light Quanta Max Planck believed that light existed as continuous waves. However, he proposed that atoms emit and absorb light in little chunks – quanta (pl. of quantum) Einstein further proposed that light itself is composed of quanta (now called photons) A quantum is an elementary unit (smallest amount) of something Mass, electric charge, light, energy, and angular momentum are all quantized Only a whole number of quanta can exist

16. Light Quanta Photons have no rest energy Photons move at speed of light The energy of a photon is its kinetic energy (E) The photon’s energy is directly proportional to its frequency E = hf (h is Planck’s constant) is the smallest amount of energy that can be converted to light of frequency f Light is a stream of photons, each with an energy hf

17. Photoelectric Effect

18. The photoelectric effect refers to the emission of electrons from the surface of a metal in response to incident light Energy is absorbed by electrons within the metal, giving the electrons sufficient energy to be 'knocked' out of the surface of the metal

19. Photoelectric Effect Maxwell wave theory of light predicts that the more intense the incident light the greater the average energy carried by an ejected (photoelectric) electron Experiment shows that the energies of the emitted electrons to be independent of the intensity of the incident radiation Einstein (1905) resolved this paradox by proposing that the incident light consisted of individual quanta, called photons, that interacted with the electrons in the metal like discrete particles, rather than as continuous waves

20. Photoelectric Effect For a given frequency of the incident radiation, each photon carried the energy E = hf, where h is Planck's constant and f is the frequency

21. Photoelectric Effect Light travels as a wave Light interacts with matter as a stream of particles

22. Waves vs. Particles

23. Images made by a digital camera. In each successive image, the dim spot of light has been made even dimmer by inserting semitransparent absorbers like the tinted plastic used in sunglasses

24. Waves vs. Particles Which model can explain the phenomenon?

25. Waves vs. Particles If light was a wave, then the absorbers would simply cut down the wave's amplitude across the whole wavefront The digital camera's entire chip would be illuminated uniformly But figures show that some pixels take strong hits while others pick up no energy at all Instead of the wave picture, the image that is naturally evoked by the data is something more like a hail of bullets from a machine gun Each "bullet" of light apparently carries only a tiny amount of energy – light is consist of a stream of particles

26. Waves vs. Particles Electron beam is directed toward a crystal

27. Waves vs. Particles Diffraction & interference pattern is observed

28. Waves vs. Particles The behavior of a particle of matter (in this case the incident electron) can be described by a wave Electrons behave like a wave!

29. Waves vs. Particles If waves can have particle properties, cannot particles have wave property? De Broglie answered this question in 1924 He suggested that all matter (electrons, protons, atoms, marbles, cars, and even human) have wave properties This phenomenon is commonly known as the wave- particle duality

30. Waves vs. Particles If waves can have particle properties, cannot particles have wave property? De Broglie answered this question in 1924 He suggested that all matter (electrons, protons, atoms, marbles, cars, and even human) have wave properties This phenomenon is commonly known as the wave- particle duality

31. Material Waves

32. All matter have wave properties The wavelength of a particle is called the de Broglie wavelength A tiny particle moving at typical speed has a detectable wavelength Objects in our daily life have tiny wavelengths which are beyond detection

33. Wavelength of an Electron Need less massive object to show wave effects Electron is a very light particle Mass of electron = 9.1x10 -31 kg Larger velocity, shorter wavelength Wavelength depends on mass and velocity

34. Wavelength of a Football Example: A football’s weight is 0.4 kg and the speed is 30 m/s. Calculate the wavelength of the football Momentum:

35. Material Waves Example: Calculate the de Broglie wavelength of an electron traveling at 2% the speed of light

36. Material Waves Example: Calculate the de Broglie wavelength of an ball traveling at 330 m/s

37. Material Waves A beam of electrons behaves like a beam of light, however, the wavelength is typically thousands of times shorter than the wavelength of the visible light

38. Material Waves The electron microscope can distinguish detail not possible with optical microscopes

39. Electron Waves The Bohr’s model explained the spectra of the element. It explained why elements emitted only certain frequencies of light since electrons can only transfer among certain energy levels The model failed to explain why electrons only occupied certain energy levels I the atom Bohr showed that in such a model the electrons would spiral into the nucleus in about 10 -10 s, due to electrostatic attraction This can be resolved by viewing electrons as waves instead of particles

40. Electron Waves In 1923, de Broglie, proposed that a way to explain the discrete energy levels was that electrons behave like waves To ‘fit a wave’ around a nucleus is when the wavelength fits the circumference a whole-number of times (so called standing waves ), and these states correspond to the observed energy levels of the electrons

41. Electron Waves The radius of a ground state, n = 1, electron has a circumference of one standing wave The radius of the first excited state, n = 2, has a circumference of two standing waves

42. Electron Waves Thus, an electron's orbit cannot decay because it is constrained by its standing wave forms Only those radii whose circumferences equaled a multiple of the electron's de Broglie wavelength were permitted

43. Electron Waves De Broglie’s predictions for the electron orbits were quickly confirmed by experiment and were found to perfectly fit the observed energy levels of electrons in atoms De Broglie thus created a new field in physics, the wave mechanics, uniting the physics of energy (wave) and matter (particle). For this he won the Nobel Prize in Physics in 1929

44. Relative Sizes of Atoms

45. The radii of the electron orbits in the Bohr’s atomic model are determined by the amount of electric charge in the nucleus As the positive charge in the nucleus increased, the negative electrons also increased. The inner orbits shrink in size due to stronger electric attraction. However, it won’t shrink as much as expected due to the increasing electrons The heavier elements are not much larger in diameter than the lighter elements Each element has unique arrangement of electron orbits unique to that element

46. Relative Sizes of Atoms

47. Atomic Energy Levels & Photon Energy 47

48. Electron orbits around the nucleus and only certain orbits are stable Radiation emitted only when electron jumps from one stable orbit to another The emitted photon has an energy E photon = E initial – E final E initial E final Photon E photon Bohr’s Atomic Model 48

49. Energy level diagrams on page 3 of your reference table Quantized Energy Levels 49

50. Each atom has a set of discrete energy levels Each level has been assigned a quantum number (n) An electron transits in hydrogen between quantized energy levels Quantized Energy Levels 50

51. How many different transitions to the lower energy levels can an electron have when the electron is at n = 4? Quantized Energy Levels 51

52. How many different transitions to the lower energy levels can an electron have when the electron is at n = 4? 3 different transitions: n = 4—>n = 3 n = 4—>n = 2 n = 4—>n = 1 Quantized Energy Levels 52

53. How many different transitions to the lower energy levels can an electron have when the electron is at n = 7 ? Quantized Energy Levels 53

54. How many different transitions to the lower energy levels can an electron have when the electron is at n = 7 ? 6 different transitions Quantized Energy Levels 54

55. Calculate the energy of photons for those possible transitions form n = 4 Energy of Photons 55

56. Calculate the energy of photons for those possible transitions form n = 4 3 possible transitions: n = 4 —> n = 3 -0.85 eV – (-1.51 eV) = 0.66 eV n = 4 —> n = 2 -0.85 eV – (-3.40 eV) = 2.55 eV n = 4 —> n = 1 -0.85 eV – (-13.6 eV) = 12.75 eV Energy of Photons 56

57. How much energy is required to ionize the Hydrogen atom? Quantized Energy Levels 57

58. How much energy is required to ionize the Hydrogen atom? E > 13.6 eV Quantized Energy Levels 58

59. The electronvolt (eV) is a unit of energy It is the kinetic energy gained by an electron when it accelerates through an electric potential difference of 1 volt Since V = W/q, or W = qV, for a single electron 1 eV = 1.602×10 −19 C x 1 V ( or 1 J/C) = 1.602×10 −19 J 1 eV = 1.60 × 10 −19 J Electronvolts & Joules 59

60. Calculate the energy of photons for the transitions form n = 4 to n = 2 in joules Energy of Photons 60

61. Calculate the energy of photons for the transitions form n = 4 to n = 2 in joules n = 4 —> n = 2 -0.85 eV – (-3.40 eV) = 2.55 eV = 2.55 eV x 1.6 x 10 -19 J/eV = 4.08 x 10 -19 J Energy of Photons 61

62. How much energy (in joules) is required to ionize the Hydrogen atom? Quantized Energy Levels 62

63. How much energy (in joules) is required to ionize the Hydrogen atom? E > 13.6 eV E > 13.6 eV x 1.6 x 10 -19 J/eV E > 2.18 x 10 -18 J Quantized Energy Levels 63

64. Hydrogen emits only photons of particular energies The emitted photon has an energy E photon = E initial – E final Electron Transition 64

65. Atomic Spectrum Hydrogen emits only photons of a set of particular energy Photon energy E = hf = hc/λ ( h = 6.63 × 10 –34 Js ) It emits a set of particular wavelengths, and frequencies 65

66. Photon is emitted when electron drops from one quantum state to another Zero energy n=1 n=2 n=3 n=4 n=1 n=2 n=3 n=4 Absorbing a photon of correct energy makes electron jump to higher quantum state. Photon absorbed hf=E 2 -E 1 Photon emitted hf=E 2 -E 1 Atomic Spectrum 66

67. E photon = E initial – E final E photon = h f = h c / λ The emitted photon has a frequency and wavelength: f = E photon / h λ = h c / E photon h = 6.63 × 10 –34 Js (Plank’s constant) Electron Transition 67

68. Calculate the frequency of photons for the transitions form n = 4 to n = 2 in a hydrogen atom Frequency of Photons 68

69. Calculate the frequency of photons for the transitions form n = 4 to n = 2 in a hydrogen atom E photon = E initial – E final = -0.85 eV – (-3.40 eV) = 2.55 eV = 2.55 eV x 1.6 x 10 -19 J/eV = 4.08 x 10 -19 J f = E / h = 4.08 x 10 -19 J / 6.63 × 10 –34 Js = 6.15 x 10 14 Hz Frequency of Photons 69

70. Calculate the wavelength of photons for the transitions form n = 4 to n = 2 in a hydrogen atom Wavelength of Photons 70

71. Calculate the wavelength of photons for the transitions form n = 4 to n = 2 in a hydrogen atom E photon = E initial – E final = 4.08 x 10 -19 J λ = h c / E photon = (6.63 × 10 –34 Js) (3.00 x 10 8 m/s) / 4.08 x 10 -19 J = 4.88 x 10 –7 m Wavelength of Photons 71

72. Identify the type of photons for the transitions form n = 4 to n = 2 in a hydrogen atom Type of Photons 72

73. Identify the type of photons for the transitions form n = 4 to n = 2 in a hydrogen atom E photon = E initial – E final = 4.08 x 10 -19 J f = E / h = 6.15 x 10 14 Hz Type of Photons 73

74. Electromagnetic spectrum diagram on page 2 of your reference table Electromagnetic Spectrum 74

75. Identify the type of photons for the transitions form n = 4 to n = 2 in a hydrogen atom E photon = E initial – E final = 4.08 x 10 -19 J f = E / h = 6.15 x 10 -14 Hz According to the electromagnetic spectrum, it’s visible light (blue) Type of Photons 75

76. Atomic Energy Levels & Photon Energy What are the resources available in the reference table? How to calculate the energy of photon emitted by an electron changing its energy level? How to convert eV to Joule? How to calculate the frequency of an emitted photon? How to calculate the wavelength of an emitted photon? How to identify the type of a photon? 76

77. Extract the information of Energy Level Diagrams on your reference table Calculate the energy of photon by E photon = E initial – E final Convert the photon energy from eV to Joule by 1 eV = 1.60 × 10 −19 J Calculate the photon frequency by f = E photon / h Calculate the photon wavelength by λ = h c / E photon Identify the type of a photon according to the electromagnetic spectrum on your reference table Steps of Solving Energy Level Problems 77

78. Quantum Physics

79. Newtonian laws that work so well for the macroworld of our daily life do not apply to events in the microworld of atom Classic mechanics is for macroworld as quantum mechanics is for the microworld Measurements in the macroworld is based on certainty while the measurements in the microworld is governed by probability

80. Heisenberg Uncertainty Principle Using –  x = position uncertainty –  p = momentum uncertainty Heisenberg showed that the product (  x )  (  p ) is always greater than ( h / 4  ) Planck’s constant

81. Q & A

82. The End