Chapter 10

1. Chapter 10 Atomic Physics

2. The quantum hypothesis • By the end of the 1800’s, physics had made significant progress. • Some physicists feared “that all of their questions might soon be answered.” • But some problems defied solution: • blackbody radiation, • photoelectric effect, and • atomic spectra.

3. Blackbody radiation • Everything around you is constantly emitting electromagnetic (EM) radiation. • A perfectly “black” body would: • absorb all light and other EM radiation incident upon it, and • be a perfect emitter of EM radiation. • Such an object is called a blackbody. • The EM radiation emitted by it is called blackbody radiation (BBR).

4. Blackbody radiation, cont’d • The characteristics of BBR emitted at a particular frequency can be illustrated with a graph of the radiation intensity versus wavelength. • Such a graph is called a blackbody radiation curve.

5. Blackbody radiation, cont’d • This graph illustrates two important ways that BBR changes when the temperature of the body is increased. • More energy is emitter per second at each wavelength of EM radiation, and

6. Blackbody radiation, cont’d • The wavelength at which the most energy is emitted per second shifts to smaller values. • In other words, the peak of the BBR curve moves toward smaller wavelengths as the temperature increases.

7. Blackbody radiation, cont’d • The principles of electromagnetism explain some of this: • A blackbody emits radiation since the atoms and molecules are continually oscillating. • Recall that a vibrating electric charge emits EM radiation. • But some things could not be answered. • An explicit explanation of the two mentioned features could not be resolved.

8. Blackbody radiation, cont’d • A “solution” was devised in 1900 by the German physicist Max Planck. • He developed a mathematical equation that accurately fit the blackbody radiation curve. • This gives the correct formula but no physical insight. • He then developed a model that would produce the desired equation. • He did not believe the model was physical even though it gave the right answer.

9. Blackbody radiation, cont’d • He proposed that an oscillating atom in a blackbody can only exchange certain fixed values of energy. • It can have zero energy, or a particular energy E, or 2E, or 3E, …. • This means that the energy of each atomic oscillator is quantized. • The energy E is called the fundamental quantum of energy for the oscillator.

10. Blackbody radiation, cont’d • The idea of quantization can be illustrated with the following figure. • On the right, the cat can rest at any height above the floor. • On the left, the cat can only rest at certain heights above the floor.

11. Blackbody radiation, cont’d • This means that: • The left cat’s potential energy can only assume certain values. • The right cat’s potential energy can assume any value.

12. Blackbody radiation, cont’d • Planck determined that the basic quantum of energy is proportional to the oscillator’s frequency: • The constant h is called Planck’s constant. • The allowed energies are then

13. The photoelectric effect • The second phenomenon defying classical explanation was the photoelectric effect. • The effect occurs when certain EM radiation illuminates a metal then electrons are ejected from the metal. • The EM wave gives energy to the electrons and allows them to escape the metal.

14. The photoelectric effect, cont’d • Albert Einstein extended Planck’s quantum hypothesis to solve this problem. • Planck suggested that light is emitted in discrete bundles of energy. • Einstein took this one step farther. • He proposed that the light remains in these bundles of energy and is absorbed in this form.

15. The photoelectric effect, cont’d • He suggested that the amount of energy in one bundle of energy of frequency f is • This allows us to visualize the wave as being composed of individual particles of energy, now called photons.

16. The photoelectric effect, cont’d • This allowed all aspects of the photoelectric effect to be understood. • Higher-frequency light ejects electrons with more energy because each photon has more energy to impart to the electron. • Bright light simply means more photons strike the metal so that more electrons are emitted per second but does not increase their energy.

17. The photoelectric effect, cont’d • The energy of a single photon is miniscule. • A convenient unit is the electron-Volt (eV). • One electron-volt is the potential energy of each electron in a 1-volt battery.

18. ExampleExample 10.1 Compare the energies associated with a quantum of each of the following types of EM radiation.

19. ExampleExample 10.1 ANSWER: For red light:

20. ExampleExample 10.1 ANSWER: For blue light:

21. ExampleExample 10.1 ANSWER: For an x ray:

22. ExampleExample 10.1 DISCUSSION: Notice the significant increase in the energy of the x ray compared to the visible light. This explains why high doses of x rays can do serious damage to living cells.

23. Applications of the photoelectric effect • The photoelectric effect is the key to “interfacing” light with electricity. • The figure shows a schematic of a device that can detect light.

24. Applications of the photoelectric effect, cont’d • When light strikes the metal plate, electrons are emitted. • The electrons are pushed across the tube because of the potential difference.

25. Applications of the photoelectric effect, cont’d • The flow of electrons “closes” the circuit. • The ammeter then measures the current flow due to the electrons. • Since there is a current, there is light.

26. Applications of the photoelectric effect, cont’d • A similar approach works for photocopiers.

27. Atomic spectra • The third problem that classical physics could not resolve is the emission spectra of the elements. • Imagine shining the light from a heated filament through a prism. • The light is separated into a range of colors. • This spectrum is called a continuous spectrum since it is a continuous band of colors.

28. Atomic spectra, cont’d • Now imagine heating a gas-filled tube. • The gas will emit some EM radiation. • After this light passes through a prism, only certain lines of color appear.

29. Atomic spectra, cont’d • This type of spectrum is called an emission-line spectrum. • Because it is due to the light emitted by the gas and it is not continuous.

30. Atomic spectra, cont’d • Here are some emission spectra for various elements. • Notice that each has its own distinct sets of lines.

31. Bohr model of the atom • Bohr constructed a model of the atom called the Bohr model: • The atom forms a miniature “solar system.” • the nucleus is at the center and the electrons move about the nucleus in well-defined orbits. • The electron orbits are quantized. • the electrons can only be in certain orbits about a given atomic nucleus. • Electrons may “jump” from one orbit to another.

32. Bohr model of the atom, cont’d • Here is a figure that illustrates the Bohr model. • The electron orbits the nucleus. • The electron can only orbit in specific orbits.

33. Bohr model of the atom, cont’d • Transitions from one orbit to another involve discrete amounts of energy. • The energy to change levels is the difference in the two energy levels.

34. Bohr model of the atom, cont’d • Let’s consider hydrogen. • One electron and one proton. • Orbit 1 is the innermost orbit and corresponds to the lowest energy state of the electron. • The amount of energy required to just remove an electron from the proton is the ionization energy. • The electron is no longer bound to the nucleus. • The atom is ionized because there is no longer the same number of electrons and protons.

35. Bohr model of the atom, cont’d • Imagine an electron that is in the sixth allowed orbit. • So it has energy E6. • Let the electron make a transition to the second orbit. • So it has energy E2. • The electron must lose energy in the amount

36. Bohr model of the atom, cont’d • This is called a radiative transition because the electron loses energy by emitting a photon of the appropriate energy. • The change in energy of the electron must equal the photon energy: • This gives a formula for the frequency of the emitted light according to which orbits are involved in the transition.

37. Bohr model of the atom, cont’d • The frequency of the emitted light is proportional to the energy of the electron orbits involved in the transition. • A downward electron transition can also occur during a collision with another particle. • A collisional transition.

38. Bohr model of the atom, cont’d • An atom can also absorb a photon. • The electron can gain energy from the incoming photon. • This increase in the electron’s energy causes it to transition to a higher energy orbit.

39. Bohr model of the atom, cont’d • If broad-spectrum light is passed through a material, the light will cause transitions to higher energy orbits. • This reduces the number of photons of the corresponding energy.

40. Bohr model of the atom, cont’d • The spectrum emerging from the material has dark bands at certain frequencies. • This type of spectrum is called an absorption spectrum.

41. Bohr model of the atom, cont’d • One unexplained result of the Bohr model was that the angular momentum of the electron in its orbit is quantized. • Mathematically, this means the allowed angular momentum can only have the values:

42. Quantum mechanics • Even with its shortcomings, the Bohr model indicated that new physics was needed to describe the atom. • Louis de Broglie proposed that electrons have wavelike properties. • We know that light has wave-like properties. • diffraction, refraction, etc. • We also know light has particle-like properties. • blackbody radiation, photoelectric effect, etc.

43. Quantum mechanics, cont’d • He suggested that the wavelength of a particle depends on its momentum. • Recall that momentum is the product of mass and velocity. • So the higher the momentum, the shorter the wavelength. • That means the higher the frequency.

44. ExampleExample 10.2 What is the de Broglie wavelength of an electron with speed 2.19×106 m/s? (This is the approximate speed of an electron in the smallest orbit in hydrogen.) The electron mass is 9.11×10-31 kg.

45. ExampleExample 10.2 ANSWER: The problem gives us: The de Broglie wavelength is then:

46. ExampleExample 10.2 DISCUSSION: This wavelength is on the same length scale as the diameter of atoms. Thus electrons are useful for probing the structure of atoms.

47. Quantum mechanics, cont’d • Experiments were performed by shooting electrons and x-rays through a solid. • The same diffraction pattern was obtained.

48. Quantum mechanics, cont’d • de Broglie’s hypothesis was also able to explain Bohr’s quantized orbits. • Since the electron acts like a wave, the wave must fit along the circumference of the electron’s orbit. • This means that only orbits with whole-numbered multiples of the wavelength are valid.

49. Quantum mechanics, cont’d • Since the circumference must equal some multiple of the wavelength: • This means • This supports the Bohr model.

50. ExampleExample 10.3 Using the results of Example 10.2, find the radius of the smallest orbit in the hydrogen atom.