Chapter 7 The Quantum-Mechanical Model of the Atom

1. Chemistry: A Molecular Approach, 1st Ed.Nivaldo Tro Chapter 7The Quantum-Mechanical Model of the Atom Roy Kennedy Massachusetts Bay Community College Wellesley Hills, MA 2007, Prentice Hall

2. The Behavior of the Very Small • electrons are incredibly small • a single speck of dust has more electrons than the number of people who have ever lived on earth • electron behavior determines much of the behavior of atoms • directly observing electrons in the atom is impossible, the electron is so small that observing it changes its behavior Tro, Chemistry: A Molecular Approach

3. A Theory that Explains Electron Behavior • the quantum-mechanical model explains the manner electrons exist and behave in atoms • helps us understand and predict the properties of atoms that are directly related to the behavior of the electrons • why some elements are metals while others are nonmetals • why some elements gain 1 electron when forming an anion, while others gain 2 • why some elements are very reactive while others are practically inert • and other Periodic patterns we see in the properties of the elements Tro, Chemistry: A Molecular Approach

4. The Nature of Lightits Wave Nature • light is a form of electromagnetic radiation • composed of perpendicular oscillating waves, one for the electric field and one for the magnetic field • an electric field is a region where an electrically charged particle experiences a force • a magnetic field is a region where an magnetized particle experiences a force • all electromagnetic waves move through space at the same, constant speed • 3.00 x 108 m/s in a vacuum = the speed of light, c Tro, Chemistry: A Molecular Approach

5. Speed of Energy Transmission Tro, Chemistry: A Molecular Approach

6. Electromagnetic Radiation Tro, Chemistry: A Molecular Approach

7. Characterizing Waves • the amplitude is the height of the wave • the distance from node to crest • or node to trough • the amplitude is a measure of how intense the light is – the larger the amplitude, the brighter the light • the wavelength, (l) is a measure of the distance covered by the wave • the distance from one crest to the next • or the distance from one trough to the next, or the distance between alternate nodes Tro, Chemistry: A Molecular Approach

8. Wave Characteristics Tro, Chemistry: A Molecular Approach

9. Characterizing Waves • the frequency, (n) is the number of waves that pass a point in a given period of time • the number of waves = number of cycles • units are hertz, (Hz) or cycles/s = s-1 • 1 Hz = 1 s-1 • the total energy is proportional to the amplitude and frequency of the waves • the larger the wave amplitude, the more force it has • the more frequently the waves strike, the more total force there is Tro, Chemistry: A Molecular Approach

10. The Relationship Between Wavelength and Frequency • for waves traveling at the same speed, the shorter the wavelength, the more frequently they pass • this means that the wavelength and frequency of electromagnetic waves are inversely proportional • since the speed of light is constant, if we know wavelength we can find the frequency, and visa versa Tro, Chemistry: A Molecular Approach

11. n (s-1) l (m) l (nm) Example 7.1- Calculate the wavelength of red light with a frequency of 4.62 x 1014 s-1 Given: Find: n = 4.62 x 1014 s-1 l, (nm) Concept Plan: Relationships: l∙n = c, 1 nm = 10-9 m Solve: Check: the unit is correct, the wavelength is appropriate for red light Tro, Chemistry: A Molecular Approach

12. Practice – Calculate the wavelength of a radio signal with a frequency of 100.7 MHz Tro, Chemistry: A Molecular Approach

13. n (MHz) n (s-1) l (m) Practice – Calculate the wavelength of a radio signal with a frequency of 100.7 MHz Given: Find: n = 100.7 MHz l, (m) Concept Plan: Relationships: l∙n = c, 1 MHz = 106 s-1 Solve: Check: the unit is correct, the wavelength is appropriate for radiowaves Tro, Chemistry: A Molecular Approach

14. Color • the color of light is determined by its wavelength • or frequency • white light is a mixture of all the colors of visible light • a spectrum • RedOrangeYellowGreenBlueViolet • when an object absorbs some of the wavelengths of white light while reflecting others, it appears colored • the observed color is predominantly the colors reflected Tro, Chemistry: A Molecular Approach

15. Amplitude & Wavelength

16. Electromagnetic Spectrum Tro, Chemistry: A Molecular Approach

17. Continuous Spectrum Tro, Chemistry: A Molecular Approach

18. The Electromagnetic Spectrum • visible light comprises only a small fraction of all the wavelengths of light – called the electromagnetic spectrum • short wavelength (high frequency) light has high energy • radiowave light has the lowest energy • gamma ray light has the highest energy • high energy electromagnetic radiation can potentially damage biological molecules • ionizing radiation Tro, Chemistry: A Molecular Approach

19. Thermal Imaging using Infrared Light Tro, Chemistry: A Molecular Approach

20. Using High Energy Radiationto Kill Cancer Cells Tro, Chemistry: A Molecular Approach

21. Interference • the interaction between waves is called interference • when waves interact so that they add to make a larger wave it is called constructive interference • waves are in-phase • when waves interact so they cancel each other it is called destructive interference • waves are out-of-phase Tro, Chemistry: A Molecular Approach

22. Interference Tro, Chemistry: A Molecular Approach

23. Diffraction • when traveling waves encounter an obstacle or opening in a barrier that is about the same size as the wavelength, they bend around it – this is called diffraction • traveling particles do not diffract • the diffraction of light through two slits separated by a distance comparable to the wavelength results in an interference pattern of the diffracted waves • an interference pattern is a characteristic of all light waves Tro, Chemistry: A Molecular Approach

24. Diffraction Tro, Chemistry: A Molecular Approach

25. 2-Slit Interference Tro, Chemistry: A Molecular Approach

26. The Photoelectric Effect • it was observed that many metals emit electrons when a light shines on their surface • this is called the Photoelectric Effect • classic wave theory attributed this effect to the light energy being transferred to the electron • according to this theory, if the wavelength of light is made shorter, or the light waves intensity made brighter, more electrons should be ejected • remember: the energy of a wave is directly proportional to its amplitude and its frequency • if a dim light was used there would be a lag time before electrons were emitted • to give the electrons time to absorb enough energy Tro, Chemistry: A Molecular Approach

27. The Photoelectric Effect Tro, Chemistry: A Molecular Approach

28. The Photoelectric EffectThe Problem • in experiments with the photoelectric effect, it was observed that there was a maximum wavelength for electrons to be emitted • called the threshold frequency • regardless of the intensity • it was also observed that high frequency light with a dim source caused electron emission without any lag time Tro, Chemistry: A Molecular Approach

29. Einstein’s Explanation • Einstein proposed that the light energy was delivered to the atoms in packets, called quanta or photons • the energy of a photon of light was directly proportional to its frequency • inversely proportional to it wavelength • the proportionality constant is called Planck’s Constant, (h)and has the value 6.626 x 10-34 J∙s Tro, Chemistry: A Molecular Approach

30. number photons l(nm) l (m) Ephoton Example 7.2- Calculate the number of photons in a laser pulse with wavelength 337 nm and total energy 3.83 mJ Given: Find: l = 337 nm, Epulse = 3.83 mJ number of photons Concept Plan: Relationships: E=hc/l, 1 nm = 10-9 m, 1 mJ = 10-3 J, Epulse/Ephoton = # photons Solve: Tro, Chemistry: A Molecular Approach

31. Practice – What is the frequency of radiation required to supply 1.0 x 102 J of energy from 8.5 x 1027 photons? Tro, Chemistry: A Molecular Approach

32. number photons Ephoton n (s-1) What is the frequency of radiation required to supply 1.0 x 102 J of energy from 8.5 x 1027 photons? Given: Find: Etotal = 1.0 x 102 J, number of photons = 8.5 x 1027 n Concept Plan: Relationships: E=hn, Etotal = Ephoton∙# photons Solve: Tro, Chemistry: A Molecular Approach

33. Ejected Electrons • 1 photon at the threshold frequency has just enough energy for an electron to escape the atom • binding energy, f • for higher frequencies, the electron absorbs more energy than is necessary to escape • this excess energy becomes kinetic energy of the ejected electron Kinetic Energy = Ephoton – Ebinding KE = hn - f Tro, Chemistry: A Molecular Approach

34. Spectra • when atoms or molecules absorb energy, that energy is often released as light energy • fireworks, neon lights, etc. • when that light is passed through a prism, a pattern is seen that is unique to that type of atom or molecule – the pattern is called an emission spectrum • non-continuous • can be used to identify the material • flame tests • Rydberg analyzed the spectrum of hydrogen and found that it could be described with an equation that involved an inverse square of integers Tro, Chemistry: A Molecular Approach

35. Emission Spectra Tro, Chemistry: A Molecular Approach

36. Hg He H Exciting Gas Atoms to Emit Light with Electrical Energy Tro, Chemistry: A Molecular Approach

37. Oxygen spectrum Neon spectrum Examples of Spectra Tro, Chemistry: A Molecular Approach

38. Na K Li Ba Identifying Elements with Flame Tests Tro, Chemistry: A Molecular Approach

39. Emission vs. Absorption Spectra Spectra of Mercury Tro, Chemistry: A Molecular Approach

40. Bohr’s Model • Neils Bohr proposed that the electrons could only have very specific amounts of energy • fixed amounts = quantized • the electrons traveled in orbits that were a fixed distance from the nucleus • stationary states • therefore the energy of the electron was proportional the distance the orbital was from the nucleus • electrons emitted radiation when they “jumped” from an orbit with higher energy down to an orbit with lower energy • the distance between the orbits determined the energy of the photon of light produced Tro, Chemistry: A Molecular Approach

41. Bohr Model of H Atoms Tro, Chemistry: A Molecular Approach

42. Wave Behavior of Electrons • de Broglie proposed that particles could have wave-like character • because it is so small, the wave character of electrons is significant • electron beams shot at slits show an interference pattern • the electron interferes with its own wave • de Broglie predicted that the wavelength of a particle was inversely proportional to its momentum Tro, Chemistry: A Molecular Approach

43. however, electrons actually present an interference pattern, demonstrating the behave like waves if electrons behave like particles, there should only be two bright spots on the target Electron Diffraction Tro, Chemistry: A Molecular Approach

44. m, v l (m) Example 7.3- Calculate the wavelength of an electron traveling at 2.65 x 106 m/s Given: Find: v = 2.65 x 106 m/s, m = 9.11 x 10-31 kg (back leaf) l, m Concept Plan: Relationships: l=h/mv Solve: Tro, Chemistry: A Molecular Approach

45. Practice - Determine the wavelength of a neutron traveling at 1.00 x 102 m/s(Massneutron = 1.675 x 10-24 g) Tro, Chemistry: A Molecular Approach

46. m(g) m (kg), v l (m) Practice - Determine the wavelength of a neutron traveling at 1.00 x 102 m/s Given: Find: v = 1.00 x 102 m/s, m = 1.675 x 10-24 g l, m Concept Plan: Relationships: l=h/mv, 1 kg = 103 g Solve: Tro, Chemistry: A Molecular Approach

47. Complimentary Properties • when you try to observe the wave nature of the electron, you cannot observe its particle nature – and visa versa • wave nature = interference pattern • particle nature = position, which slit it is passing through • the wave and particle nature of nature of the electron are complimentary properties • as you know more about one you know less about the other Tro, Chemistry: A Molecular Approach

48. Uncertainty Principle • Heisenberg stated that the product of the uncertainties in both the position and speed of a particle was inversely proportional to its mass • x = position, Dx = uncertainty in position • v = velocity, Dv = uncertainty in velocity • m = mass • the means that the more accurately you know the position of a small particle, like an electron, the less you know about its speed • and visa-versa Tro, Chemistry: A Molecular Approach

49. Uncertainty Principle Demonstration any experiment designed to observe the electron results in detection of a single electron particle and no interference pattern Tro, Chemistry: A Molecular Approach

50. Determinacy vs. Indeterminacy • according to classical physics, particles move in a path determined by the particle’s velocity, position, and forces acting on it • determinacy = definite, predictable future • because we cannot know both the position and velocity of an electron, we cannot predict the path it will follow • indeterminacy = indefinite future, can only predict probability • the best we can do is to describe the probability an electron will be found in a particular region using statistical functions Tro, Chemistry: A Molecular Approach