224AExamSampleQuestions

# 224AExamSampleQuestions - upper state of energy to the...

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Phys 224A Relevant past exam questions not previously given in Sample Exams p. 1 of 1 2c) (7 pts) When the total number of units of energy q=U / ! is much smaller than the number of atoms N in a three-dimensional Einstein solid with level spacing ! , one can show that the total energy U of the entire system is U=(3N ! ) exp(- ! / k b T). Show that this result gives the same average energy per oscillator that you would find for a two level system with level spacing ! in contact with an energy reservoir at very low temperature T. d) (8 points) It should be no surprise that a two level system can behave very differently than a harmonic oscillator in an Einstein solid. For a two level system find the ratio of the probability of being in the
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Unformatted text preview: upper state of energy ! to the probability of being in the lower state of energy 0 at high temperatures (kb)T >> ! . Determine the average energy of a two level system at high T. 3) (10 pts) Imagine that an atom has exactly two energy levels whose energy difference is 0.015 eV. At what temperature will there be two atoms in the higher state for every three in the lower state? 4) (10 pts) Consider the average energy of a harmonic oscillator relative to its lowest level. Let the energy level spacing be ! and k B be Boltzmann's constant. For a given temperature T, what is the approximate ratio of ! /(k B T) that produces an average energy of approximately 0.6(kb)T?...
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