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Homework Help: Mass of Hydrogen needed to determine lifetime of proton

  1. Oct 25, 2017 #1
    1. The problem statement, all variables and given/known data

    The current limit on the proton’s lifetime is determined by observing a large body of water for a long time and noticing that no one of the hydrogen nuclei in H2O have decayed. Assuming that the experiment making this measurement has been going on for 10 years, how many tons of water are needed to set the constraint on the lifetime of the proton τ > 1034 years?

    2. Relevant equations

    N = N0e-t/τ

    3. The attempt at a solution

    For this I would think we would use this equation to then find the amount of protons needed to make -t/τ = -(10)/(1034 and then from that figure out the number of protons in H2O and then figure out how many molecules then multiply by the molecular weight. Am I on the right track?
  2. jcsd
  3. Oct 26, 2017 #2


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    2017 Award

    Staff: Mentor

    That will work. You don't even need the full exponential function as the observation time is so tiny compared to the lifetime.

    If you expect one decay (at a given lifetime value) and observe no decay, that is not sufficient to rule out this value (you could have been just a bit unlucky), but that is probably a technical detail you don't have to worry about here.
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