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Q & A: Nucleons sticking and decaying

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Most recent answer: 10/22/2007
Q:
Q1: What keeps the two quarks in a proton together? Q2: Carbon-14 is radioactive but Carbon-12 isn’t. Why should having two extra neutrons in the nucleus make Carbon-14 unstable?
- Muhammed (age 17)
Sir George Monoux College, London
A:
Hi Muhammed,

Q1:

There are actually "three" quarks in a proton -- two up-type quarks and one down-type quark. These are held together by the strong nuclear force. Quarks have electrical charge (up-type quarks have charge 2/3, and down-type quakrs have charge -1/3. In these units, electrons have charge -1), and also a different kind of charge, whimsically called "color". Electrically charged particles interact electromagnetically (attracting or repelling) by exchanging photons. Color-charged particles interact with each other by exchanging gluons. Gluons are a lot like photons (they're massless, they carry a fundamental force), and also a bit unlike photons, in that gluons themselves have color charge. This last property means that gluons interact with each other, while photons, being neutral, do not. Gluons, because they interact with each other, make a sticky mess, holding the quarks together. In fact, no one has ever observed any particle with a net color charge -- the three quarks in a proton have colors which add up to a net color charge of zero. Try to pull one of the quarks out by hitting it, and you end up stretching the gluon mess, and by stretching it enough you give it enough energy to make new particles, instead of just pulling out one of the quarks.

Q2:

If left alone, neutrons will decay, with an average lifetime of 886 seconds. They decay into a proton, an electron, and an electron antineutrino. Neutrons are just a very tiny bit heavier than protons, and so this reaction is allowed. This reaction proceeds via the weak nuclear force, by the exchange of a charged W boson.

Neutrons bound up in atomic nuclei sit in energy levels determined by quantum mechanics (just like the electrons in orbit around the nucleus). In stable nuclei, like Carbon 12, the neutrons cannot decay, because to do so, the resulting proton would have to be put into a higher energy level than the neutron was in that it came from. The Pauli exclusion principle says that energy levels "fill up", and the lowest unfilled one gets the proton from the neutron decay. If the energy difference between the neutron's level and the proton's level, plus the energy needed to make the electron and the antineutrino is bigger than the mass difference between the neutron and the proton (E=mc^2 after all), then the decay won't happen.

Carbon 14 has more neutrons than protons, and so the state the proton goes into isn't much different in energy than the state the neutron was in in the first place. This decay proceeds at a very slow rate, though -- C14 it has a lifetime measured in thousands of years.

Tom J.

(published on 10/22/2007)

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