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Unformatted text preview: Modern Physics1 A Brief History of Modern Physics and the development of the Schrödinger Equation "Modern" physics means physics discovered after 1900; i.e. twentiethcentury physics. 1900: Max Planck (German) tried to explain blackbody radiation using Maxwell's equations and statistical mechanics and found that he could not. He could only reproduce the experimentallyknown BB spectrum by assuming that the energy in an electromagnetic wave of frequency f is quantized according to EM wave E n h f = , where n = 1, 2, 3, … and h = Planck's constant = 6.6 × 10 34 (SI units) Planck regarding this as a math trick; he was baffled by its physical significance. 1905: Albert Einstein , motivated in part by Planck's work, invents the concept of a photon to explain the photoelectric effect. A photon is a quantum (packet) of electromagnetic radiation, with energy E h f γ = = ϖ h . 1911: Ernest Rutherford (New Zealand/Britain) shows that an atom consists of a small, heavy, positivelycharged nucleus, surrounded by small light electrons. But there is a problem with the classical theory of this nuclear atom: An electron in orbit about a nucleus is accelerating and, according to Maxwell's equations, an accelerating charge must radiate (give off EM radiation). As the electron radiates, giving energy, it should spiral into the nucleus. 1913: Niels Bohr (Danish), a theorist working in Rutherford's lab, invents the Bohr model. This is essentially a classical model, treating the electron as a particle with a definite position and momentum, but the model has two nonclassical, ad hoc assumptions: 1) The angular momentum of the electron is quantized: L n = h . 2) The electron orbits, determined by (1), are stable ("stationary"), do not radiate, unless there is a transition between two orbits, and then the atom emits or absorbs a single photon of energy f i h f E E = The predictions of Bohr model match the experimental spectrum of hydrogen perfectly. It is important to remember that the Bohr model is simple, useful, and wrong . For instance, it predicts that the ground state of the Hatom has angular momentum L = h , when in fact, the ground state of the H atom (sstate) has L = 0. The Bohr model is a semiclassical model , meaning it combines aspects of classical and quantum mechanics. Semiclassical models are frequently used by physicists because they are heuristically useful (easy to understand and often give correct results). But they must always be used Last update: 2/27/2012 Dubson Phys3220 Notes, University of Colorado Classically, an electron in an atom should radiate and spiral inward as it loses energy. Modern Physics2...
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 Fall '08
 STEVEPOLLOCK
 Radiation, Louis de Broglie, Erwin Rudolf Josef Alexander Schrödinger, Dubson Phys3220 Notes

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