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phys 369 09 hw 4 - Phys 369 Fall 2009 Homework#4 Due Monday...

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Phys. 369, Fall 2009 Homework #4 Due: Monday, Sept. 28, beginning of class 100 points total 1. (18 points) A 4 He atom has “spin-0”, which means that its internal state is non-degenerate. Therefore the Sackur-Tetrode equation gives the correct entropy of a gas of 4 He. However, a 3 He atom has spin ½ (from the spin of its nucleus). This means that it has two spin energy levels, and , separated in energy by 2 μ B, where μ is the magnetic moment of the 3 He nucleus and B is the magnetic field. The Sackur-Tetrode equation does not correctly give the entropy of a gas of 3 He atoms because it does not take the two different spin states into account. a) Assume that the magnetic field B = 0, so that the two spin states and have exactly zero energy. Assume that there is no constraint on the number of spins in the state. What is the multiplicity of a gas containing N 3 He atoms in a box of volume V, and with total energy between U and U + dU, taking into account the effect of the atomic spin?
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