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PS2_Chem288 - Spring 2005 Problem Set 2 Handed out Thursday...

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Spring 2005 Problem Set 2 Chemistry 288 – Marohn Handed out: Thursday, 3 February 2005 Due: Thursday, 10 February 2005 1. Sharpness of the probability function for a large collection of two-level systems. We derived in class that P ( N, s ) = radicalbigg 2 πN e - 2 s 2 /N is the probability that N spins can be in a configuration having spin excess 2 s . Take N = 10 6 . (a) Sketch P ( N, s ) versus s . What is the allowed range of s ? (b) At what s does P ( N, s ) fall to 1 /e of its maximum value? 2. Large collection of two-state atoms. Consider a molecule that is well approximated as having two electronic states, a ground state of energy E 0 = 0 and an excited state of energy E 1 = 1 eV. Suppose that the molecule must be in either its ground state or its excited state. Consider a collection of N = 6 . 02 × 10 23 such molecules. (a) What are the two most im probable configurations? Sketch them. What are their energies? (b) What is the most probable configuration? Sketch it. What is its energy?
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