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Experiments in Quantum Mechanics

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Colorado State University
PH 122
Brian Jones

Light as a Particle Light can be thought of as consisting of photons, “packets” of energy, which are quantized, and have energies given by the following equation: c E = hf = h λ 1240eV nm E (in eV) = λ(¿nm) In many modern sources of light, photons of light are produced by electrons making energy level transitions. Electrons can also make transitions between energy levels in atoms, as well as molecules we model as “particles in a box”. If you have a transition between E and E 2 1 the photon will not have an energy equal to E or 1 , bu2 rather the difference between the energy levels: E transitionn2-n1or n1, 2 … Energy Transitions – The Hydrogen Atom Electrons in atoms are constrained to be near the nucleus. This constraint causes them to exist in certain quantized energy states. Passing a current through a gas in a tube causes electrons to jump to higher energy states then fall back down to the lowest energy state, the ground state. As they do so, they emit a photon with an energy equivalent to the difference in energy between the two states. Energy levels is different for each element → each element has a characteristic emission spectrum Energy levels for hydrogen follow the equation: 4 me 1 E n - 8ε h n2 2 = -13.6 eV ( n2 ) for n = 1, 2, 3… 0 All of these energy levels are negative. E = 0 eV corresponds to a free electron; these are bound states of the electron. Energy Transitions – Particle in a Box Particles have a wave nature. If you trap a particle in a “box,” the wave will only have certain states available to it – quantized energy states. For a particle in a one-dimensional box of length L, these energy levels are given by: h2 E n1 2 n1
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