This, and the next two questions, are about Gibbs factors and the grand cannonical 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 -0.5 eV. What is the probability that a given site will have a Xe atom occupying it?

This, and the next two questions, are about Gibbs factors and the grand cannonical 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 -0.5 eV. What is the probability that a given site will have a Xe atom occupying it?