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ps2 - Chem 120B Problem Set 2 Due February 4 2011 1...

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Chem 120B Problem Set 2 Due: February 4, 2011 1. Problems 17-8 and 17-43 in McQuarrie & Simon’s Physical Chemistry textbook. For problem 17-8, note that the two spin states of a proton in a magnetic field have energies ± planckover2pi1 γB z / 2 . Calculate the field strength B z for which the number of protons aligned with the field is twice that of protons aligned against the field, N w = 2 N o , at T = 300 K . 2. Consider a particle of mass m in a uniform gravitational field. Its potential energy is E ( h ) = mgh , where h is the height above sea level and g is the earth’s gravitational constant, g = 9 . 8 m/s 2 . (i) According to the Boltzmann distribution, what is the probability p ( h ) of finding the particle at height h , relative to the probability p (0) of finding it at sea level ( h = 0 ), at temperature T ? [In truth, p ( h ) is a probability density , since h is a continuous variable. A more proper way to word this question would be in terms of the probability p ( h h of finding the particle in a small range of height between h and h h . But since ( p ( h h ) / ( p (0)Δ h ) = p ( h ) /p (0) , the answer would be the same.] (ii) Now imagine that there are N such masses, all identical and non-interacting. On average, how many of these objects reside at height h , relative to the number at sea level? Express your answer in terms of relative densities, ρ ( h ) (0) , where ρ ( h ) denotes the average number of particles per unit

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ps2 - Chem 120B Problem Set 2 Due February 4 2011 1...

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