Is whole Carbon 13 atom (not just the nucleus) a fermion or boson?

In summary, the conversation discusses whether it is simple to determine if a particle is a fermion or a boson by adding up the spins of the elementary particles and checking for integer or half-integer values. The conversation also mentions alternative methods involving nuclear spin and electronic spin. Ultimately, the conversation concludes that it is as simple as adding up the spins, but may involve complications with nuclear shell structure.
  • #1
ygolo
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This ought to be simple, I think. But I haven't found a consistent way to think about things yet.

Is it as simple as adding up all the spins of the elementary particles in the particle and checking whether the total has inter or half-integer spin?

Homework Statement



State whether the following is a fermion or a boson:
(a) an electron
(b) a proton
(c) a neutron
(d) a photon
(e) a carbon 12 nucleus
(f) a carbon 13 nucleus
(g) a carbon 12 atom
(h) a carbon 13 atom
(i) a Nitrogen 14 atom
(j) a Nitrogen 15 atom

Homework Equations



So I was never taught the basics, I am taking a graduate physical chemistry class coming from an electrical engineering background. Most of the things are rather easy, but sometimes I don't know the theory involved.

So I formed 2 possible ways to approach this (one simple, the other more involved):

1) Just add up the spins of the elementary particles and check if the result is half integer or integer.

2) Based on some other reading I did on the web, it seems like:
(a) For nuclear spin, if Z is even and A is even, I=0. For other cases, I need to look it up.
(b) For electronic spin, pair up electrons using Hund's rule, Pauli Exclusion principle, etc. Then S=0.5*(# of unpaired electrons)
(c) In an atom, electron spin dominates (because the electronic magentic moment is 100x larger)

Of course, if I ignore (c), and the nuclear spin is half-integer only when A is odd, these methods will give the same answers.

The Attempt at a Solution



The following give the same answers either way:
(a) fermion
(b) fermion
(c) fermion
(d) boson
(e) boson
(f) fermion
(g) boson

(i) fermion

The following, however, disagree depending on which way I interpret things.

(h) 1) The sum of spins of elementary particles is an odd multiple of 1/2. So from this I would say fermion.
2) But the ground state electronic configuration has two unpaired electrons, and if the electronic spins dominate, this would be a boson

(j) 1) The sum of spins of elementary particles is an even multiple of 1/2. So from this I would say boson.
2) But the ground state electronic configuration has three unpaired electrons, and if the electronic spin dominates, this would say fermion.
 
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  • #2
ygolo said:
Is it as simple as adding up all the spins of the elementary particles in the particle and checking whether the total has inter or half-integer spin?

If you mean "adding the spins of the electrons, protons and neutrons in an atom", then yes. For example, Helium-3 is a fermion but Helium-4 is a boson. (Bare in mind that protons and neutrons are not elementary particles.)

If you want to get into all the complications of nuclear shell structure, then you'd need to take a course on nuclear physics, but I doubt it is necessary for your problem.
 
Last edited:

1. Is a whole Carbon 13 atom a fermion or boson?

A whole Carbon 13 atom is a fermion.

2. What determines whether an atom is a fermion or boson?

The number of protons, neutrons, and electrons in an atom determine whether it is a fermion or boson. If the total number of these particles is odd, the atom is a fermion. If the total number is even, the atom is a boson.

3. Why is a Carbon 13 atom considered a fermion?

A Carbon 13 atom has an odd number of particles (6 protons, 7 neutrons, and 6 electrons), making it a fermion according to the Pauli exclusion principle. This principle states that no two identical fermions can occupy the same quantum state simultaneously.

4. What are the properties of a fermion?

Fermions are particles with half-integer spin, meaning they have an intrinsic angular momentum. They also follow the Pauli exclusion principle, meaning they cannot occupy the same quantum state simultaneously.

5. How do fermions behave compared to bosons?

Fermions behave differently from bosons due to their different spin and the Pauli exclusion principle. For example, fermions make up matter and have a tendency to repel each other, while bosons make up energy and have a tendency to attract each other.

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