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Beta+ decay or electron capture?

  1. Apr 4, 2015 #1
    1. The problem statement, all variables and given/known data
    CoMlzye.jpg

    2. Relevant equations
    See below.

    3. The attempt at a solution
    We have β+ decay ##X_{Z}^{A} \rightarrow Y_{Z-1}^{A}+ e^{+}+\upsilon _{e}## which leads to the mass condition ##M(A,Z)>m(A,Z-1)+2m_{e}##.

    We have electron capture ##X_{Z}^{A} + e^{-}\rightarrow Y_{Z-1}^{A}+ \upsilon _{e}## which leads to the mass condition ##M(A,Z)>m(A,Z-1)+\frac{\varepsilon }{c^{2}}##.

    Those are the mass conditions. From my notes it says ##\frac{\varepsilon }{c^{2}}\ll m(A,Z-1)## therefore electron capture can happen whenever β+ decay does, but β+ decay is more likely. I am unsure about this statement or how it helps distinguish which one would happen for certain conditions.

    Any ideas would really be appreciated.
     
  2. jcsd
  3. Apr 4, 2015 #2

    mfb

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    Staff: Mentor

    You can check the inequalities to see what is possible.
    If beta+ decay is possible (and if the inequality is not too close to an equality), it is more likely.
     
  4. Apr 4, 2015 #3
    the inequalities are ##\frac{\varepsilon }{c^{2}}## and ##2m_{e}## , sorry it should have been if ##\frac{\varepsilon }{c^{2}}\ll 2m_{e}## in the original post. So if ##\frac{\varepsilon }{c^{2}}\ll 2m_{e}## then it's beta decay, if ##\frac{\varepsilon }{c^{2}}\gg 2m_{e}## it's electron capture and if they are equal it is equally likely? Is that what you mean?

    Many thanks for the reply
     
  5. Apr 4, 2015 #4

    mfb

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    Staff: Mentor

    That does not make sense.

    If both inequalities are satisfied, both processes are possible. Then beta+ decay is more likely, with an exception:
    If beta+ is "just" allowed (the left side of the beta+ inequality condition is just a tiny bit larger than the right), then beta+ decay is not very likely.
     
  6. Apr 4, 2015 #5
    Ahh so by stating the mass condition for each I've answered the question, excellent, I think I got confused by trying to link the two mass conditions somehow as independant entities when they can both be satisfied at the same time. thanks again.
     
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