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Unformatted text preview: CHEM 356, Lecture 3, Fall 2009 1 Einstein (1916) : utilized Plancks hypothesis to study the probability of radiative transitions for a system in equilibrium with EM radiation. Model . EM field: photon gas with energy density ( , ) Matter: atoms, 1 with energy 1 , 2 with energy 2 and, for convenience, 2 > 1 . photons with energy = 2 1 can: be absorbed by atoms in state with energy 1 A( 1 ) + A( 2 ) induce atoms in state with energy 2 to emit photons of energy A( 2 ) + A( 1 ) + 2 . An important property of photons radiated by induced (or stimulated) emission is that they are in phase with one another: we say that they are coherent . Einstein also assumed that spontaneous transitions can occur from the higher energy state to the lower energy state, but NOT in the opposite direction: A( 2 ) A( 1 ) + CHEM 356, Lecture 3, Fall 2009 2 The probabilities for these three events to happen are given by (a) 12 ( , ) = probability for stimulated absorption of a photon by an atom in energy state 1 (b) 21 ( , ) = probability for stimulated emission of a photon from an atom in energy state 2 (c) 21 = probability for spontaneous emission of a photon by an atom in energy state...
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