Quantum Gases - Mixing of 3He and 4He

[i_hate_math]

Homework Statement

Consider a solution in which 99% of the atoms are ⁴He and 1% are ³He. Assuming that the ³He atoms behave as an ideal gas of spin-1/2 particles determine the Fermi energy of the ³He atoms. You may assume that one mole of ⁴He occupies a volume of 28 cm³.

Homework Equations

E_F = h²/2m * (3π²n)^2/3

The Attempt at a Solution

The density of ⁴He is calculated using its molar volume:
n₄ = 2.151*10²⁸ [m^-3]

Assuming equilibrium, the concentration of ⁴He is:
x₄ = n₄/(n₃+n₄) = 0.01

=> n₃ = n₄/99

=> E_F = h²/2m * (3π²n₃)^2/3

This approach seems too simple for an exam question on quantum gases as I haven't considered the fact that ⁴He are bosons and undergo BEC when T->0.

 

[mfb]

Why would you need to care about He-4? An ideal gas of He-3 shouldn't care about other atoms.