Chapter 30 Quantum Physics

Transcription

1 Chapter 30 Quantum Physics Units of Chapter 30 Blackbody Radiation and Planck s Photons and the Photoelectric Effect The Mass and Momentum of a Photon Photon Scattering and the Compton Effect Units of Chapter 30 The de Broglie Hypothesis and Wave- The Heisenberg Uncertainty Principle Quantum Tunneling Development of Quantum Physics Problems remained from classical mechanics that relativity didn t explain Blackbody Radiation The electromagnetic radiation emitted by a heated object Photoelectric Effect Emission of electrons by an illuminated metal Spectral Lines Emission of sharp spectral lines by gas atoms in an electric discharge tube Development of Quantum Physics 1900 to 1930 Development of ideas of quantum mechanics Also called wave mechanics Highly successful in explaining the behavior of atoms, molecules, and nuclei Quantum Mechanics reduces to classical mechanics when applied to macroscopic systems Involved a large number of physicists Planck introduced basic ideas Mathematical developments and interpretations involved such people as Einstein, Bohr, Schrödinger, de Broglie, Heisenberg, Born and Dirac An ideal blackbody absorbs all the light that is incident upon it. 1

2 An ideal blackbody is also an ideal radiator. If we measure the intensity of the electromagnetic radiation emitted by an ideal blackbody, we find: Classical physics calculations were completely unable to produce this temperature dependence, leading to something called the ultraviolet catastrophe. Rayleigh -Jeans Planck 8π f 3 c k T 8 hf πf kbt 1 hf ( e 1) 3 c B Planck discovered that he could reproduce the experimental curve by assuming that the radiation in a blackbody came in quantized energy packets, depending on the frequency: 30- Photons and the Photoelectric Effect The photoelectric effect occurs when a beam of light strikes a metal, and electrons are ejected. Each metal has a minimum amount of energy required to eject an electron, called the work function, W 0. If the electron is given an energy E by the beam of light, its maximum kinetic energy is: The constant h in this equation is known as Planck s constant: 30- Photons and the Photoelectric Effect Classical predictions: 1. Any beam of light of any color can eject electrons if it is intense enough.. The maximum kinetic energy of an ejected electron should increase as the intensity increases. Observations: 1. Light must have a certain minimum frequency in order to eject electrons.. More intensity results in more electrons of the same energy. 30- Photons and the Photoelectric Effect Einstein suggested that the quantization of light was real; that light came in small packets, now called photons, of energy: A more intense beam of light will contain more photons, but the energy of each photon does not change. Example: A laser emits.5 W of light energy at the wavelength of 53 nm, determine the number of photons given off by the laser per second.

3 30- Photons and the Photoelectric Effect Explanations: Each photon s energy is determined by its frequency. If it is less than the work function, electrons will not be ejected, no matter how intense the beam The Mass and Momentum of a Photon Photons always travel at the speed of light (of course!). What does this tell us about their mass and momentum? The total energy can be written: Example: A sodium surface is illuminated with light of wavelength 300 nm. The work function of solium is.46 ev. Calculate (a) the energy of each photon in electron volts, (b) the maximum kinetic energy of the ejected photoelectrons, and (c) the cutoff wavelength for the sodium. Since the left side of the equation must be zero for a photon, it follows that the right side must be zero as well The Mass and Momentum of a Photon Energy-momentum equation in Relativity: E = E + 0 p c 30-4 Photon Scattering and the Compton Effect The Compton effect occurs when a photon scatters off an atomic electron. With E 0 = m 0 c = 0, And finally, 30-4 Photon Scattering and the Compton Effect In order for energy to be conserved, the energy of the scattered photon plus the energy of the electron must equal the energy of the incoming photon. This means the wavelength of the outgoing photon is longer than the wavelength of the incoming one: In 193, de Broglie proposed that, as waves can exhibit particle-like behavior, particles should exhibit wave-like behavior as well. He proposed that the same relationship between wavelength and momentum should apply to massive particles as well as photons: 3

4 Indeed, we can even perform Young s twoslit experiment with particles of the appropriate wavelength and find the same diffraction pattern. This is even true if we have a particle beam so weak that only one particle is present at a time we still see the diffraction pattern produced by constructive and destructive interference. Also, as the diffraction pattern builds, we cannot predict where any particular particle will land, although we can predict the final appearance of the pattern. These images show the gradual creation of an electron diffraction pattern. The correctness of this assumption has been verified many times over. One way is by observing diffraction. We already know that X-rays can diffract from crystal planes: Low Energy Electron Diffraction (LEED) pattern from Silicon (111) surface. Example: A beam of neutrons with a de Broglie wavelength of 0.40 nm diffracts from a crystal of table salt, which has an interionic spacing of 0.83 nm. (a) What is the speed of the neutrons? (b) What is the angle of the second interference maximum? The same patterns can be observed using either particles or X-rays. The uncertainty just mentioned that we cannot know where any individual electron will hit the screen is inherent in quantum physics, and is due to the wavelike properties of matter. 4

5 When the electrons diffract through the slit, they acquire a y-component of momentum that they had not had before. This leads to the uncertainty principle: If we know the position of a particle with greater precision, its momentum is more uncertain; if we know the momentum of a particle with greater precision, its position is more uncertain. Mathematically, The uncertainty principle can be cast in terms of energy and time rather than position and momentum: Thought Experiment the Uncertainty Principle The effects of the uncertainty principle are generally not noticeable in macroscopic situations due to the smallness of Planck s constant, h. A thought experiment for viewing an electron with a powerful microscope In order to see the electron, at least one photon must bounce off it During this interaction, momentum is transferred from the photon to the electron Therefore, the light that allows you to accurately locate the electron changes the momentum of the electron 30-7 Quantum Tunneling Waves can tunnel through narrow gaps of material that they otherwise would not be able to traverse. As the gap widens, the intensity of the transmitted wave decreases exponentially Quantum Tunneling Given their wavelike properties, it is not surprising that particles can tunnel as well. A practical application is the scanning tunneling microscope, which can image single atoms using the tunneling of electrons. 5

6 An ideal blackbody absorbs all light incident on it. The distribution of energy within it as a function of frequency depends only on its temperature. Frequency of maximum radiation: Planck s hypothesis: Light is composed of photons, each with energy: In terms of wavelength: Photoelectric effect: photons eject electrons from metal surface. Minimum energy: work function, W 0 Minimum frequency: Photons have zero rest mass. Photon momentum, frequency, and wavelength: de Broglie hypothesis: particles have wavelengths, depending on their momentum: Compton effect: a photon scatters off an atomic electron, and exits with a longer wavelength: Both X-rays and electrons can be diffracted by crystals. Light and matter display both wavelike and particle-like properties. The position and momentum of waves and particles cannot both be determined simultaneously with arbitrary precision: Nor can the energy and time: Particles can tunnel through a region that classically would be forbidden to them. 6