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Unformatted text preview: Chemistry 21b Problem set # 3 Out: 19 January 2011 Due: 26 January 2011 Problems are worth: 1a=10, 1b=10, 1c=10, 1d=10; 2a=15, 2b=15; 3a=10, 3b=10, 3c=10. 1. At low temperatures, the rotational part of the partition function Q ( T ) = ∞ summationdisplay J =0 (2 J + 1)exp(- E J /kT ) dominates the non-translational degrees of freedom, where E J = BJ ( J + 1) cm − 1 for a simple diatomic or linear molecule in a 1 Σ (that is, closed shell) electronic state. Roughly, this function tells you over how many states the population is distributed, and is central to the Boltzmann distribution ( N J /g J ) = ( N/Q ) e − E J /kT , where N J =population in state J , g J =degeneracy of state J , E J =energy of state J , N =total population, and Q =the partition function) and statistical thermodynamics, as you’ll see later in Ch 21c (or may already know). (a.) Derive an alternative, approximate form of this partition function by replacing the summation with an integral and by taking J to be a continuous variable. This formula should depend onlyto be a continuous variable....
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This note was uploaded on 01/03/2012 for the course CH 21b taught by Professor List during the Fall '10 term at Caltech.
- Fall '10