In “Direct Measurement of the Size of the Helium Dimer” by F. Luo, C. F. Geise, and W. R. Gentry [J. Chemical Physics 104 (1996): 1151], evidence for the helium dimer is presented. As one can imagine, the chemical bond in the dimer is extremely weak, with an estimated value of only 8.3mJ/mol.

a. An estimate for the bond length of 65 Å is presented in the paper. Using this information, determine the rotational constant for He₂. Using this value for the rotational constant, determine the location of the first rotational state. If correct, you will determine that the first excited rotational level is well beyond the dissociation energy of He₂.

b. Consider the following equilibrium between He₂ and its atomic constituents:

He₂ (g) ⇄ 2He (g)

If there are no rotational or vibrational states to consider, the equilibrium is determined exclusively by the translational degrees of freedom and the dissociation energy of He₂. Using the dissociation energy provided earlier and V = 1000. cm³, determine K_P assuming that T = 10.K. The experiments were actually performed at 1 mK; why was such a low temperature employed?