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•• Consider a simple solid, such as aluminum, consisting of N identical atoms. Assume that the Einstein approximation correctly describes the vibrational motion of the atom. (a) Assume that the vibrational level spacing has the value ε = 0.037 eV (a typical value in a solid) and consider the probability that an atom of the solid is in its ground state. At what temperature is this probability equal to 0.1? (b) For a given N and ε, how high does the temperature have to be to ensure that effectively no atoms are in the ground state? Is this temperature achievable in an ordinary sample of a solid?
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