Chapter 7 The Quantum–Mechanical Model of the Atom

1. Chemistry: A Molecular Approach, 2nd Ed.Nivaldo Tro Chapter 7The Quantum–Mechanical Model of the Atom Roy Kennedy Massachusetts Bay Community College Wellesley Hills, MA

2. The Beginnings of Quantum Mechanics • Until the beginning of the 20th century it was believed that all physical phenomena were deterministic • Work done at that time by many famous physicists discovered that for sub-atomic particles, the present condition does not determine the future condition • Albert Einstein, Neils Bohr, Louis de Broglie, Max Planck, Werner Heisenberg, P. A. M. Dirac, and Erwin Schrödinger • Quantum mechanics forms the foundation of chemistry – explaining the periodic table and the behavior of the elements in chemical bonding – as well as providing the practical basis for lasers, computers, and countless other applications Tro: Chemistry: A Molecular Approach, 2/e

3. 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 • even shining a light on the electron would affect it Tro: Chemistry: A Molecular Approach, 2/e

4. A Theory that Explains Electron Behavior • The quantum-mechanical model explains the manner in which electrons exist and behave in atoms • It helps us understand and predict the properties of atoms that are directly related to the behavior of the electrons • why some elements are metals and others are nonmetals • why some elements gain one electron when forming an anion, whereas others gain two • 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, 2/e

5. The Nature of Light:Its 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 a 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, 2/e

6. Electromagnetic Radiation Tro: Chemistry: A Molecular Approach, 2/e

7. Speed of Energy Transmission Tro: Chemistry: A Molecular Approach, 2/e

8. 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, 2/e

9. Wave Characteristics Tro: Chemistry: A Molecular Approach, 2/e

10. 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 of the waves and the frequency • the larger the amplitude, the more force it has • the more frequently the waves strike, the more total force there is Tro: Chemistry: A Molecular Approach, 2/e

11. 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 • because the speed of light is constant, if we know wavelength we can find the frequency, and vice versa Tro: Chemistry: A Molecular Approach, 2/e

12. 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) Conceptual 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, 2/e

13. Practice – Calculate the wavelength of a radio signal with a frequency of 100.7 MHz Tro: Chemistry: A Molecular Approach, 2/e

14. 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) Conceptual 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, 2/e

15. 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 and reflects others, it appears colored • the observed color is predominantly the colors reflected Tro: Chemistry: A Molecular Approach, 2/e

16. Amplitude & Wavelength Tro: Chemistry: A Molecular Approach, 2/e

17. The Electromagnetic Spectrum • Visible light comprises only a small fraction of all the wavelengths of light – called the electromagnetic spectrum • Shorter wavelength (high-frequency) light has higher 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, 2/e

18. low frequency and energy high frequency and energy Types of Electromagnetic Radiation • Electromagnetic waves are classified by their wavelength • Radiowaves = l > 0.01 m • Microwaves = 10−4 < l < 10−2 m • Infrared (IR) • far = 10−5 < l < 10−4 m • middle = 2 x 10−6 < l < 10−5 m • near = 8 x 10−7< l < 2 x 10−6m • Visible = 4 x 10−7 < l < 8 x 10−7 m • ROYGBIV • Ultraviolet (UV) • near = 2 x 10−7 < l < 4 x 10−7 m • far = 1 x 10−8 < l < 2 x 10−7 m • X-rays = 10−10 < l < 10−8m • Gamma rays = l < 10−10 Tro: Chemistry: A Molecular Approach, 2/e

19. Electromagnetic Spectrum Tro: Chemistry: A Molecular Approach, 2/e

20. Continuous Spectrum Tro: Chemistry: A Molecular Approach, 2/e

21. Thermal Imaging using Infrared Light Tro: Chemistry: A Molecular Approach, 2/e

22. Sunburns Caused by High-Energy UV Radiation Tro: Chemistry: A Molecular Approach, 2/e

23. Using High-Energy Radiationto Kill Cancer Cells Tro: Chemistry: A Molecular Approach, 2/e

24. 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, 2/e

25. Interference Tro: Chemistry: A Molecular Approach, 2/e

26. 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, 2/e

27. Diffraction Tro: Chemistry: A Molecular Approach, 2/e

28. 2-Slit Interference Tro: Chemistry: A Molecular Approach, 2/e

29. 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 • this idea predicts if a dim light were 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, 2/e

30. The Photoelectric Effect Tro: Chemistry: A Molecular Approach, 2/e

31. The Photoelectric Effect:The Problem • In experiments it was observed that there was a minimum frequency needed before electrons would be emitted • called the threshold frequency • regardless of the intensity • It was also observed that high-frequency light from a dim source caused electron emission without any lag time Tro: Chemistry: A Molecular Approach, 2/e

32. 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 is directly proportional to its frequency • inversely proportional to its 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, 2/e

33. l(nm) l(m) Ephoton number photons 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 Conceptual Plan: Relationships: E=hc/l, 1 nm = 10−9 m, 1 mJ = 10−3 J, Etotal=Ephoton # photons Solve: Tro: Chemistry: A Molecular Approach, 2/e

34. 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, 2/e

35. Practice – What is the frequency of radiation required to supply 1.0 x 102 J of energy from 8.5 x 1027 photons? number photons Ephoton n(s−1) Given: Find: Etotal = 1.0 x 102 J, number of photons = 8.5 x 1027 n Conceptual Plan: Relationships: E=hn, Etotal = Ephoton∙# photons Solve: Tro: Chemistry: A Molecular Approach, 2/e

36. Practice – Order the following types of electromagnetic radiation:microwaves, gamma rays, green light, red light, ultraviolet light • By wavelength (short to long) • By frequency (low to high) • By energy (least to most) gamma < UV < green < red < microwaves microwaves < red < green < UV < gamma microwaves < red < green < UV < gamma Tro: Chemistry: A Molecular Approach, 2/e

37. Ejected Electrons • One photon at the threshold frequency gives the electron just enough energy for it to escape the atom • binding energy, f • When irradiated with a shorter wavelength photon, 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, 2/e

38. Suppose a metal will eject electrons from its surface when struck by yellow light. What will happen if the surface is struck with ultraviolet light? • No electrons would be ejected. • Electrons would be ejected, and they would have the same kinetic energy as those ejected by yellow light. • Electrons would be ejected, and they would have greater kinetic energy than those ejected by yellow light. • Electrons would be ejected, and they would have lower kinetic energy than those ejected by yellow light. • No electrons would be ejected. • Electrons would be ejected, and they would have the same kinetic energy as those ejected by yellow light. • Electrons would be ejected, and they would have greater kinetic energy than those ejected by yellow light. • Electrons would be ejected, and they would have lower kinetic energy than those ejected by yellow light. Tro: Chemistry: A Molecular Approach, 2/e 38

39. Spectra • When atoms or molecules absorb energy, that energy is often released as light energy • fireworks, neon lights, etc. • When that emitted light is passed through a prism, a pattern of particular wavelengths of light 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 Tro: Chemistry: A Molecular Approach, 2/e

40. Exciting Gas Atoms to Emit Light with Electrical Energy Tro: Chemistry: A Molecular Approach, 2/e

41. Na K Li Ba Identifying Elements with Flame Tests Tro: Chemistry: A Molecular Approach, 2/e

42. Emission Spectra Tro: Chemistry: A Molecular Approach, 2/e

43. Examples of Spectra Tro: Chemistry: A Molecular Approach, 2/e

44. Emission vs. Absorption Spectra Spectra of Mercury Tro: Chemistry: A Molecular Approach, 2/e

45. Rydberg’s Spectrum Analysis Johannes Rydberg (1854–1919) • 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, 2/e

46. Rutherford’s Nuclear Model • The atom contains a tiny dense center called the nucleus • the volume is about 1/10 trillionth the volume of the atom • The nucleus is essentially the entire mass of the atom • The nucleus is positively charged • the amount of positive charge balances the negative charge of the electrons • The electrons move around in the empty space of the atom surrounding the nucleus Tro: Chemistry: A Molecular Approach, 2/e

47. Problems with Rutherford’s Nuclear Model of the Atom • Electrons are moving charged particles • According to classical physics, moving charged particles give off energy • Therefore electrons should constantly be giving off energy • should cause the atom to glow! • The electrons should lose energy, crash into the nucleus, and the atom should collapse!! • but it doesn’t! Tro: Chemistry: A Molecular Approach, 2/e

48. The Bohr Model of the Atom Neils Bohr (1885–1962) • The nuclear model of the atom does not explain what structural changes occur when the atom gains or loses energy • Bohr developed a model of the atom to explain how the structure of the atom changes when it undergoes energy transitions • Bohr’s major idea was that the energy of the atom was quantized, and that the amount of energy in the atom was related to the electron’s position in the atom • quantized means that the atom could only have very specific amounts of energy Tro: Chemistry: A Molecular Approach, 2/e

49. Bohr’s Model • The electrons travel in orbits that are at a fixed distance from the nucleus • stationary states • therefore the energy of the electron was proportional to the distance the orbit was from the nucleus • Electrons emit radiation when they “jump” from an orbit with higher energy down to an orbit with lower energy • the emitted radiation was a photon of light • the distance between the orbits determined the energy of the photon of light produced Tro: Chemistry: A Molecular Approach, 2/e

50. Bohr Model of H Atoms Tro: Chemistry: A Molecular Approach, 2/e