1. You are studying a molecule which can exist in either anon-degenerate singlet

Question

1. You are studying a molecule which can exist in either anon-degenerate singlet state or a triplet state (degeneracy = 3).The triplet state is higher in energy than the singletby . Assuming the molecules are localized andindependent, a) find the expression for the molecular partitionfunction, and b) get an expression in terms of forCv and solve it at T = /k

Explanation / Answer

Partition function =gi*exp(-)    wheregi is degeneracy Let E be energy of triplet above singlet, so E = 0 is defined forthe singlet Partition function = 1*exp(0) + 3*exp(-*) Partition function = Q = 1 + 3*exp(-) b) = i*gi*exp(-i) =-dQ/d => -dQ/d = i*gi*exp(-i) Cv = d/dT d/d = d/d(1/kT) =-k*T2*d/dT = -k*T2*Cv -k*T2*Cv = d/d =-d2Q/d2 k*T2*Cv = d2Q/d2 = 3*2*exp(-) Cv = (3/k)(/T)2*exp(-) At T = /k = 1/kT = 1/ Cv = (3/k)*(/[/k])2 *exp(-/) Cv = (3k)*exp(-1)

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