Quantum Gases - Mixing of 3He and 4He

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SUMMARY

The discussion focuses on calculating the Fermi energy of 3He atoms in a mixture where 99% of the atoms are 4He. The relevant formula used is EF = h²/2m * (3π²n)²/³, where n represents the number density of 3He. The density of 4He is determined to be n4 = 2.151 x 10²⁸ m⁻³, leading to the concentration of 4He as x4 = n4/(n3+n4) = 0.01. The participant expresses concern that the simplistic approach may overlook the implications of 4He being bosons and their behavior at low temperatures, specifically regarding Bose-Einstein Condensation (BEC).

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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


EF = 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

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

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