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I Nuclear decay

  1. Mar 18, 2017 #1
    Given that an unstable particle has a constant probability of decaying per unit time, why is it said that its chance of surviving falls exponentially?
     
  2. jcsd
  3. Mar 18, 2017 #2

    BvU

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    It's like froth on beer: the more there is, the more there decays.
    Or (in the other direction) like money accumulating on a bank: the more there is, the more interest (in absolute sense) you get, which gains interest again, etc.

    Probability ##p## is given, number of decays is proportional to number of particles ##N##, so $$ {dN\over dt} = - p N $$.

    At an "I" level you can solve this kind of differential equation
     
  4. Mar 18, 2017 #3

    mfb

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    It has a constant probability to decay per unit time if it still lives. This survival probability goes down over time, therefore the probability to see a decay after time x goes down with increasing x. If you solve the differential equation, you see that it goes down exponentially.
     
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