Helium-3 & Helium-4: Bosonic vs. Fermionic Properties

[Char. Limit]

OK, I understand, mostly, about isotope differences. What I don't get is why Helium-3 is considered a fermion, and Helium-4 is considered a boson. Why is this, and what possible effects does this have?

Some explanation on what defines bosons and fermions would also be useful.

 

[NanakiXIII]

The relevant property separating bosons from fermions in this case is that bosons have integer spin (0, 1, 2, ...), while fermions have half-integer spin (1/2, 3/2, 5/2, ...). If you don't know what spin is, you'll probably need to learn a little more before returning to this question.

Adding up spins is a little tricky, but suffice to say that when you add two particles together that both have half-integer spin (two fermions), you get a particle with integer spin (a boson).

Helium-3 is a fermion, and Helium-4 just has one extra neutron compared to Helium-3. Neutrons are also fermions. So, you add two fermions together and thus get a boson.

 

[Char. Limit]

OK, so far I'm with you...

Now, does this change the properties of Helium-3?

 

[f95toli]

Well, fermions don't like to mix. So a good example of the difference between these isotopes is that He-3 won't become superfluid until you cool it to less than 3 mK, whereas He-4 becomes a superfluid (which sort of means it forms a bosonic condensate) at 2.2K.

 

[NanakiXIII]

Multiple fermions are not allowed to be in the same quantum state together - there's only room for one. This is called the Pauli exclusion principle. No such law exists for bosons. This, for example, means that if you have a system of bosons, all of them can be in the quantum state with lowest possible energy. For fermions, it may be that they need to occupy quantum states with increasingly higher energies, because there's no room for them in the lower-energy states. This, for example, is what keeps a neutron star from caving in under its own gravity.

That being what it is, I'm not sure whether any of this applies to Helium in practice. These things only become important at high density, when the particles come close enough for quantum effects to be important. If you're thinking of ordinary chemistry, none of the above plays any significant part, I would guess. The main difference that might matter there is the mass.

 

[f95toli]

That being what it is, I'm not sure whether any of this applies to Helium in practice.

It certainly does, a practical example is that most methods for cooling samples to low temperatures (below 1.7K) relies on using both He-4 and He-3. The simplest way of doing it is to keep the isotopes completely separate and first condense He-3 by cooling it by pumped He-4, and then in turn pump on the He-3; this will allow you to reach temperatures of about 250mK.
For even lower temperatures you can use a nice thermodynamics "tricks" where the enthalpy of mixing of He-3 and He-4 is used, this is how dilution refrigerators work and they've been the "workhorses" for all experiments done at very low temperatures for the last 30 years or so. A "normal" dil fridge will reach about 25 mK with the experimental wiring in place (although it is possible to reach lower temperatures, below 10mK)