Saturday, August 15, 2009

Bosons or Fermions?

A class of particles which have an integer spin are called bosons. Example - photon, etc. Any number of bosons can go to the same quantum state. Thus they are friendly to each other ! They obey Bose-Einstein statistics. The wave function associated with bosons is symmetric.

A class of particles which have a half- integer spin are called fermions. Example - proton, neutron, electron, etc. Unlike bosons, only two fermions (at maximum) can go to the same quantum state, as dictated by the Pauli Exclusion Principle. They obey Fermi-Dirac statistics. The wave function associated with fermions is anti-symmetric.

An atom can also be classified as a composite boson or a composite fermion.  To find whether an atom is a composite boson or a composite fermion, you need to look at the net spin of the atom due to its constituent particles that make it. For example, consider the simplest of the atoms - Hydrogen. Hydrogen has a proton and an electron. A proton is a half-integer particle and so is an electron. Therefore, the net spin of a normal hydrogen atom is one, which is an integer. Therefore, hydrogen is a composite boson. If we consider a helium-4 atom, there are two protons, two neutrons and two electrons. Each of these particles has a half integer spin. Therefore, the net spin of a normal helium atom is an integer. Hence, helium is a composite boson. What's about lithium-7 ? A lithium-7 atom has three protons, four neutrons and three electrons. Therefore, the net spin of a lithium-7 atom is an integer and hence it is a composite boson. On the other hand, by the same way of reasoning, lithium-6 is a composite fermion.

In general,  an atom can be classified as a composite boson or a composite fermion on the basis of  the total number of constituent particles contained in it. If the total number of constituent particles  is even it is a composite boson where as if the total number of constituent particles is odd, it is a composite fermion !


11 comments:

Unknown said...

It is so simple and easy to understand.I was a bit confused how the spin is determined for atoms and classified as boson and fermions.This article helps a lot.

Ritaban said...

why you said if a particle has even no of nucleon then it is fermion? 4He have 2 proton 2 neutron and 2 electrons that is even no of nucleons but they are bosons....I want to clear this contradiction.please give me answer.

RKafle said...

Hi Ritaban,

Thanks for your comment.

I mentioned a general rule in my posting which, by the way, applies in most of the atoms. For example, in Sodium-23 isotope, the number of protons is 11, the number of neutrons is 12, and therefore, the number nucleons is 23 which is an odd number. Since the number of electrons in Sodium atom is 11, this makes the total number of constituent particles 34 which is even and hence Sodium atom is a composite boson. We can similarly argue for other atoms to show that they are composite bosons or composite fermions.
To remove an ambiguity, I have updated my posting.

Please keep reading !

xyz said...

Is it correct to state that the number of bosons and the number of fermions are equal? At least conceptually?

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R Jay said...

Suppose we have a system of two non interacting spin half particles, then what would be the total wavefunction? Symmetric or antisymmetric?