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Early Quantum Theory. Discovery and Properties of the Electron. In the late 19 th century, discharge tubes were made that emitted “cathode rays.”. 27.1 Discovery and Properties of the Electron. It was found that these rays could be deflected by electric or magnetic fields.
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Discovery and Properties of the Electron In the late 19th century, discharge tubes were made that emitted “cathode rays.”
27.1 Discovery and Properties of the Electron It was found that these rays could be deflected by electric or magnetic fields.
Discovery and Properties of the Electron By accelerating the rays through a known potential and then measuring the radius of their path in a known magnetic field, the charge to mass ratio could be measured: (27-1) The result is
Discovery and Properties of the Electron Cathode rays were soon called electrons. Millikan devised an experiment to measure the charge on the electron by measuring the electric field needed to suspend an oil droplet of known mass between parallel plates.
Discovery and Properties of the Electron The mass and charge of each droplet were measured; careful analysis of the data showed that the charge was always an integral multiple of a smallest charge, e.
Discovery and Properties of the Electron The currently accepted value of e is: Knowing e allows the electron mass to be calculated:
Planck’s Quantum Hypothesis; Blackbody Radiation All objects emit radiation whose total intensity is proportional to the fourth power of their temperature. This is called thermal radiation; a blackbody is one that emits thermal radiation only.
Planck’s Quantum Hypothesis; Blackbody Radiation The spectrum of blackbody radiation has been measured; it is found that the frequency of peak intensity increases linearly with temperature.
Planck’s Quantum Hypothesis; Blackbody Radiation This figure shows blackbody radiation curves for three different temperatures. Note that frequency increases to the left.
Planck’s Quantum Hypothesis; Blackbody Radiation This spectrum could not be reproduced using 19th-century physics. A solution was proposed by Max Planck in 1900: The energy of atomic oscillations within atoms cannot have an arbitrary value; it is related to the frequency: The constant h is now called Planck’s constant.
Planck’s Quantum Hypothesis; Blackbody Radiation Planck found the value of his constant by fitting blackbody curves: Planck’s proposal was that the energy of an oscillation had to be an integral multiple of hf. This is called the quantization of energy.
Photon Theory of Light and the Photoelectric Effect Einstein suggested that, given the success of Planck’s theory, light must be emitted in small energy packets: (27-4) These tiny packets, or particles, are called photons.
Photon Theory of Light and the Photoelectric Effect The photoelectric effect: If light strikes a metal, electrons are emitted. The effect does not occur if the frequency of the light is too low; the kinetic energy of the electrons increases with frequency.
Photon Theory of Light and the Photoelectric Effect • If light is a wave, theory predicts: • Number of electrons and their energy should increase with intensity • Frequency would not matter
Photon Theory of Light and the Photoelectric Effect • If light is particles, theory predicts: • Increasing intensity increases number of electrons but not energy • Above a minimum energy required to break atomic bond, kinetic energy will increase linearly with frequency • There is a cutoff frequency below which no electrons will be emitted, regardless of intensity
Photon Theory of Light and the Photoelectric Effect The particle theory assumes that an electron absorbs a single photon. Plotting the kinetic energy vs. frequency: This shows clear agreement with the photon theory, and not with wave theory.
Photon Theory of Light and the Photoelectric Effect The photoelectric effect is how “electric eye” detectors work. It is also used for movie film soundtracks.
Energy, Mass, and Momentum of a Photon Clearly, a photon must travel at the speed of light. Looking at the relativistic equation for momentum, it is clear that this can only happen if its rest mass is zero. We already know that the energy is hf; we can put this in the relativistic energy-momentum relation and find the momentum: (27-6)
Compton Effect Compton did experiments in which he scattered X-rays from different materials. He found that the scattered X-rays had a slightly longer wavelength than the incident ones, and that the wavelength depended on the scattering angle: (27-7)
Compton Effect This is another effect that is correctly predicted by the photon model and not by the wave model.
Photon Interactions; Pair Production • Photons passing through matter can undergo the following interactions: • Photoelectric effect: photon is completely absorbed, electron is ejected • Photon may be totally absorbed by electron, but not have enough energy to eject it; the electron moves into an excited state • The photon can scatter from an atom and lose some energy • The photon can produce an electron-positron pair.
Photon Interactions; Pair Production In pair production, energy, electric charge, and momentum must all be conserved. Energy will be conserved through the mass and kinetic energy of the electron and positron; their opposite charges conserve charge; and the interaction must take place in the electromagnetic field of a nucleus, which can contribute momentum.
Wave-Particle Duality; the Principle of Complementarity We have phenomena such as diffraction and interference that show that light is a wave, and phenomena such as the photoelectric effect and the Compton effect that show that it is a particle. Which is it? This question has no answer; we must accept the dual wave-particle nature of light.
Wave-Particle Duality; the Principle of Complementarity The principle of complementarity states that both the wave and particle aspects of light are fundamental to its nature. Indeed, waves and particles are just our interpretations of how light behaves.
Wave Nature of Matter Just as light sometimes behaves as a particle, matter sometimes behaves like a wave. The wavelength of a particle of matter is: (27-8) This wavelength is extraordinarily small.
Wave Nature of Matter The wave nature of matter becomes more important for very light particles such as the electron.
Wave Nature of Matter Electron wavelengths can easily be on the order of 10-10 m; electrons can be diffracted by crystals just as X-rays can.
