Helium Absorption | Grand Partition Function & <N>

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    Absorption Helium
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The discussion centers on calculating the Grand Partition function for a system in thermal and diffusive equilibrium with helium gas on a metal surface. The key equation for the partition function is presented as z = Σ e^(-β(Ni)(εi-μ)). Participants express confusion about how to incorporate the states of the surface being either occupied by a helium atom or vacant. The average thermal occupancy <N> of a site is also to be derived, but the initial steps remain unclear to contributors. Clarifying these concepts is essential for solving the homework problem effectively.
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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!
 
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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
 
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