hw02 - PHYS 4050 Assignment 2 Microstates Macrostates and...

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PHYS 4050 Assignment 2 Microstates, Macrostates, and Multiplicity Due 25 September 2015 1. Suppose you flip 50 fair coins. (a) How many possible outcomes (microstates) are there? (b) How many ways are there of getting exactly 25 heads and 25 tails? (c) What is the probability of getting exactly 25 heads and 25 tails? (d) What is the probability of getting exactly 30 heads and 20 tails? (e) What is the probability of getting exactly 40 heads and 10 tails? (f) What is the probability of getting 50 heads and no tails? (g) Plot a graph of the probability of getting n heads, as a function of n . 2. For an Einstein solid with four oscillators and two units of energy, write down a diagram for each possible microstate in the form of a series of circles and vertical lines, as we used in the lecture notes to prove the multiplicity formula Ω( N, q ) = q + N - 1 q . Then count the number of diagrams to see whether it agrees with this formula. 3. Use a computer program (for example, an Excel chart) to produce a

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