A gas made up of fermions with spin 1/2 and mass m is located inside a cubic container with side L₀. The walls of the container can absorb gas: on every unit of surface there are σ (an unknown number of) sites, to each of which one fermion with energy -ε₀ can get attached. The gas is so diluted that one can assume that μ<<ε₀, where μ refers to the chemical potential of said gas. Given is also that at temperature T₀=ε₀/k the number of Fermions N_G is equal to N_s, the number of fermions that have been absorbed into the walls of the container.

a. find the surface density of absorption sites σ.

b. said gas is moved into a cubic container made of the same material, at the same temperature, but with side-length 2L₀. Calculate the relation N_G/N_s

c. said gas is moved back to the original container, while lowering the temperature to T/4. Calculate the relation N_G/N_s once more.