Question

Calculate the electronic gas pressure in metallic sodium, at `T=0` in which the concentration of free electrons is `n=2.5.10^(22)cm^(-3)`. Use the equation for the pressure of ideal gas.

Answer 1

From the kinetic theory of gasses we know
`P(2)/(3)(U)/(V)`
Here `U` is the total interval enrgy of the gas. This result is applicable to Fermi gas also Now at `T = 0`
`U=U_(0)=Nlt E gt = nVlt E gt`
so `p=(2)/(3)n lt E gt`
`=(2)/(3)nxx(3)/(5)E_(F)=(2)/(5)nE_(F)`
`=( ħ^(2))/(5m)(3pi^(2))^(2//3)n^(5//3)`
Substituting the value we get
`p= 4.92xx10^(4)` atoms