Spring 2005Problem Set 2Chemistry 288 – MarohnHanded out: Thursday, 3 February 2005Due: Thursday, 10 February 20051.Sharpness of the probability function for a large collection of two-level systems.We derived in classthatP(N, s) =radicalbigg2πNe-2s2/Nis the probability thatNspins can be in a configuration having spin excess 2s. TakeN= 106.(a) SketchP(N, s) versuss. What is the allowed range ofs?(b) At whatsdoesP(N, s) fall to 1/eof its maximum value?2.Large collection of two-state atoms.Consider a molecule that is well approximated as having two electronicstates, a ground state of energyE0= 0 and an excited state of energyE1= 1 eV. Suppose that the moleculemust be in either its ground state or its excited state. Consider a collection ofN= 6.02×1023such molecules.(a) What are the two mostimprobable configurations? Sketch them. What are their energies?(b) What is the most probable configuration? Sketch it. What is its energy?
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