3. Rotational Symmetry of H2 Due to the nuclear spin symmetry of protons, molecular hydrogen (H2) has two different forms (spin isomers): (1) ortho-H2, with nuclear spin angular momentum / = 1 (degeneracy gi = 3), requiring odd rotational angular momentum J (2) para-H2, with nuclear spin angular momentum / = 0 (degeneracy gi = 1), requiring even rotational angular momentum J A. Nuclear Spin Partition Function When no external field is applied, the nuclear spin configurations of ortho-H2 and para-H2 are degenerate with each other. Set their nuclear spin energies to EI = 0 and assume no excited states occupied, evaluate nuclear spin partition functions Ans for ortho-H2 and para- H2 separately under Boltzmann distribution. Ins = Sum[gi Exp[-BEI], I] B. Rotational Partition Function Based on the requirement of Jby ortho-H2 and para-H2, evaluate their rotational partition functions Grot separately and indicate any similarity or difference compared to diatomic molecules with no symmetry. Assume the rotational constant is B. Crot = Sum[g, Exp[-BE], J] C. Total Partition Function and Thermodynamic Properties Let's imagine a frozen crystal of H2 with distinguishable N ortho-H2 molecules and N para-H2 molecules for which all other degrees of freedom are frozen to the lowest energy level Gele = qvib = 9tra = 1 Evaluate the overall partition function, entropy, internal energy and Helmholtz free energy of this system