Problem 5.20 (Schroeder’s Intro to Thermal Physics)

Problem 5.20

The first excited energy level of a hydrogen atom has an energy of 10.2 eV, if we take the ground-state energy to be zero. However, the first excited level is really four independent states, all with the same energy. We can therefore assign it an entropy of since for this given value of the energy, the multiplicity is 4. Question: For what temperatures is the Helmholtz free energy of a hydrogen atom in the first excited level positive, and for what temperatures is it negative? (Comment: When for the level is negative, the atom will spontaneously go from the ground state into that level, since for the ground state and always tends to decrease. However, for a system this small, the conclusion is only a probabilistic statement; random fluctuations will be very significant.)

Solution:

Problem 5.20 Solution (Download)

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