# Beta+ decay or electron capture?

1. Apr 4, 2015

### rwooduk

1. The problem statement, all variables and given/known data

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. Apr 4, 2015

### 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.

3. Apr 4, 2015

### rwooduk

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

4. Apr 4, 2015

### 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.

5. Apr 4, 2015

### rwooduk

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.