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I Branching fraction

  1. Jul 11, 2018 #1
    I’ve had huge difficulty understanding/interpreting the concept of branching fraction. So correct me if I’m wrong please:
    Let’s take the decay of Ra-226 with half-life of 1602 years as an example. It decays through alpha 1 chanel to the excited state of Rn-222 with E=0,187 Mev ( branching fraction 5,4%) and through alpha 2 decay chanel to the ground state of Rn-222 ( Branching fraction 94,6%).

    Now my understanding/interpretation :
    If we have for example 10^6 Ra-226 nuclides at t=0 , then after 1602 years have passed , 0.054 * ( 10^6 / 2 )=27000 of alpha1 particles and (10^6/2)- 27000=527000 alpah 2 particles will have emitted.
     
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  3. Jul 11, 2018 #2

    BvU

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    Hello leoneul, :welcome:

    Idea's good, math is not : (10^6/2)- 27000=473000 :wink:
     
  4. Jul 11, 2018 #3
    hehe thanks alot! This simple concept has been causing so much trouble bcs some sources refers to the branching ratio as “ probability” which confused me
     
  5. Jul 11, 2018 #4

    mathman

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    For any one atom the branching ratio reflects the probabilities for the channels. Don't overthink!
     
  6. Jul 11, 2018 #5
    So for my example the probability that a certain SINGLE Ra-226 nucleus decays through alpha 1 channel is 5.4% but if we have an ENSEMBLE of Ra-226, then 5.4 % will decay through chanel 1. Correct?
     
  7. Jul 11, 2018 #6

    BvU

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    Again, idea's correct. This time the wording could be a bit sharper by expressing it as a ratio $${\alpha_1\ {\rm decays} \over {\rm total \ decays}} \times 100 \;\%$$ however, litterally taken what you write is correct (but you have to wait infinitely long ...)
     
  8. Jul 11, 2018 #7
    Understood. Thank you very much!
     
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