Quantum Gases - Mixing of 3He and 4He

In summary, the conversation discusses the determination of the Fermi energy of 3He atoms in a solution where 99% of the atoms are 4He and 1% are 3He. The calculation involves using the density of 4He and assuming equilibrium to find the concentration of 3He, which is then used to calculate the Fermi energy using a formula. The potential complications of considering 4He as bosons and their possible impact on the ideal gas of 3He are also mentioned.
  • #1
i_hate_math
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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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  • #2
Why would you need to care about He-4? An ideal gas of He-3 shouldn't care about other atoms.
 

1. What is a quantum gas?

A quantum gas is a state of matter in which particles behave according to the principles of quantum mechanics, exhibiting wave-like properties and occupying discrete energy levels. Examples include Bose-Einstein condensates and fermionic gases.

2. What is the significance of mixing 3He and 4He gases?

Mixing 3He and 4He gases allows for the study of quantum effects in a binary mixture, such as superfluidity and Bose-Einstein condensation. It also has practical applications in cryogenics and low-temperature physics.

3. How are 3He and 4He gases mixed in experiments?

In experiments, 3He and 4He gases are typically mixed by condensing them separately and then mixing them in a controlled manner. This can be achieved through techniques such as diffusion, advection, or turbulent mixing.

4. What is the behavior of a mixed 3He-4He gas at low temperatures?

At low temperatures, a mixed 3He-4He gas can exhibit interesting phenomena such as phase separation, superfluidity, and Bose-Einstein condensation. The specific behavior depends on the concentration and temperature of the mixture.

5. What are some potential applications of studying the mixing of 3He and 4He gases?

Studying the mixing of 3He and 4He gases has potential applications in fields such as low-temperature physics, cryogenics, and quantum computing. It can also provide insights into the fundamental properties of quantum gases and their behavior at extreme conditions.

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