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Homework Help: How do I determine if a certain nuclear decay is allowed?

  1. May 12, 2016 #1
    Hi, I am struggling with a question where they want me to determine whether or not three different decay are allowed.

    From what I have understood all decays must follow a set of conservation law. These laws are:
    1 Conservation of Baryon number
    2 Conservation of Lepton number
    3 Conservation of electric charge

    This is very straight forward when you have simple decays like the decay of a neutron. Where you have:

    n -> p+e+anti ve

    But how does it work for nucleons?

    For example:

    Thorium-222 -> Oxygen-16 + Lead-206

    This decay is not allowed as thorium-222 only decays with alpha-decay. But as far as I can see the laws are still followed.

    1: 222 -> 16 + 206 = 222
    2: 90 -> 8 + 82 = 90
    3: 90-90 -> 8-8 + 82-82 = 0

    What am I missing? please help!
  2. jcsd
  3. May 12, 2016 #2
    There's another requirement.
    4. Mass+energy must be conserved.

    Does Oxygen-16 + Lead-206 have more mass than Thorium-222? If so, then the decay is not allowed.
  4. May 12, 2016 #3
    I forgot to add that law.

    The mass difference is: 222.018468u - (205.974465u + 15.994914u) = 0.0491u

    Which would suggest that this decay is allowed.

    Thanks for the answer though!
  5. May 12, 2016 #4
    Are you taking into account the difference in mass between neutrons and protons? Recall that neutrons are a bit heavier than protons.
  6. May 12, 2016 #5
    Yes that difference is accounted for. I got the masses from this site/paper https://www-nds.iaea.org/amdc/ame2012/mass.mas12
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