This, and the next two questions, are about Gibbs factors and the grand canonical ensemble. To study surface physics, pure Xe gas at standard temperature (300 K) and pressure (1 atm) is in contact with a surface that has special sites manufactured to attract Xe atoms. Only a single Xe atom fits onto such a site, so a given surface site has two states: empty and full. In our derivation of the partition function of the ideal gas, we assumed that zero energy corresponds to a gas particle being at rest. Then trapped at a surface site, a Xe atom is at rest; in addition, its attraction to the surface site implies that it has negative potential energy, called a binding energy. Take the binding energy to be 0.49 eV. What is the probability that a given site will have a Xe atom occupying it? (a) At what partial pressure of Xenon would the probability you computed in the previous question be exactly 1/2? Give your answer in atmospheres. (b) Now, imagine that we replaced Xenon with a diatomic molecule of the same molecular mass. For a heavy molecule, the rotational states are very closely spaced together, and we will take Zinternal = 100 at room temperature (you can think of Zinternal as a rough count of how many quantum rotational states are thermally accessible). Assuming that a diatomic molecule has the same binding energy as a Xenon atom, what fraction of the sites will be occupied when the diatomic molecules are used in the experiment instead of Xenon atoms? A bound molecule cannot rotate. The diatomic gas is also at at standard temperature (300 K) and pressure (1 atm). (c) Redo part (b) if the diatomic molecule has four visibly different positions in which it can be trapped at a given site