Helium Absorption | Grand Partition Function & <N>

[Lyons_63]

Homework Statement

The atomic site that is in thermal and diffusive equilibrium with a gas of Helium atoms that is on the surface of a metal can either absorb an atom of Helium or it can be vacant.
(a) What is the Grand Partition function of the system?
(b) Derive the average thermal occupancy <N> of a site

Homework Equations

The Attempt at a Solution

I have no idea where to even begin!

 

[Lyons_63]

The partition function is given by z = Ʃ e^ -β (Ni) (εi-μ)
how do you account for the fact that the surface is either vacant or not