Consider an ensemble of units in which the first excited electronic state at energy ε₁is m₁-fold degenerate, and the energy of the ground state is m0 -fold degenerate with energy ε₀.

a. Demonstrate that if ε₀ = 0, the expression for the electronic partition function is

b. Determine the expression for the internal energy U of an ensemble of N such units. What is the limiting value of U as the temperature approaches zero and infinity?

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