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Homework Help: Are these Nuclear Reactions permitted?

  1. Sep 20, 2010 #1
    1. The problem statement, all variables and given/known data

    Which of the following Nuclear Reactions are allowed?

    A) e- + p --> [tex]\mu[/tex]- + p

    B) n --> p + [tex]\pi[/tex]-

    C) K- + p --> (anti)k0 + n

    2. Relevant equations

    While I don't know if there are any relevant equations, I know that there are several conservation laws that are required to make a reaction acceptable.

    3. The attempt at a solution

    A) e- + p --> [tex]\mu[/tex]- + p

    I ran through a few conservation rules.

    - I said that the Baryon number on each side was 1, so Baryon number is conserved.
    - e- and mu are both leptons, so lepton number is conserved
    - charge is conserved

    On this problem I am leaning towards it being correct, but the reason I am hesitant to say so is because I am worried I am missing a conservation law somewhere.

    B) n --> p + [tex]\pi[/tex]-

    - Again, baryon number is conserved
    - lepton number is conserved
    - mesons don't require conservation
    - the charge is conserved.

    Again, I lean towards this being correct, but I am kind of worried about how a neutron results in the formation of a proton and pi- particle, for a number of different reasons. First, I've always associated the change of the charge of a nucleon with the release or absorption of an electron - I have never heard of a different lepton taking its place. Second, there is a really large mass discrepancy, but I think that might be solvable by the fact that the neutron could have a large kinetic energy and the p and pi- particles not moving as much.

    C) K- + p --> (anti)k0 + n

    -Baryon number is conserved
    -Lepton number is conserved
    -Charge is conserved

    Am I over exaggerating in worrying that these reactions are not valid? I feel like there are too many pot-holes for a reaction to fall in, so I am really hesitant to give a definite answer.

    Would anyone be able to steer me in the right direction if more conservation laws apply here?
  2. jcsd
  3. Sep 21, 2010 #2


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    Homework Helper

    Good work so far, but you're right that you're missing a few conservation laws.

    A) Not just total lepton number is conserved, but the number for each family of leptons is also individually conserved (except by neutrino oscillations). So electron number is itself conserved, muon number is conserved, and tau number is conserved.

    B) Mesons don't require conservation, but their constituent quark flavors do. So when you have a reaction that involves hadrons (particles consisting of quarks), and it seems to satisfy other conservation laws, it's often a good idea to break the particles down into their quark content and see if you notice anything that doesn't add up there. Remember that quark-antiquark pairs can be created and can annihilate each other.

    As far as the mass/energy thing, that's definitely important to think about. Remember that if energy is to be conserved, it has to be conserved in every reference frame - specifically including the center of mass frame.

    C) This is another one where I would recommend checking the quark content.

    After enough practice with this sort of thing, you get used to remembering all the conservation laws. Off the top of my head, here are the ones I remember:
    -Angular momentum
    -6 quark flavors (up, down, strange, charm, bottom, top) [except in weak interactions]
    -3 lepton families (electron, muon, tau) [except in neutrino oscillations]
    (the last two usually take care of themselves)
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