Hi,When a nucleus does [itex]\beta[/itex]-decay[tex]_Z^A X

[A_B]

Hi,

When a nucleus does $\beta$-decay
$$_Z^A X \rightarrow _{Z+1}^A Y + e^- + \overline{\nu}$$
The daughter nucleus has one more charge than the mother nucleus, so it will take an electron into its cloud. Why is this electron's contribution to the Q-value said to cancel that from the emitted $\beta$ particle? The $\beta$ particle is created in the reaction so that obviously gives a $-m_e c^2$ in the Q-value. But the absorbed electron exists before and after the reaction, so I don't see how it should have any effect.

thanks
A_B

 

[Valerie Park]

The electron that is taken into the daughter nucleus is not created in the reaction, so it does not contribute to the mass difference between the initial and final states. However, since the nucleus gains an extra proton, the electron must be taken in to maintain the overall charge of the nucleus. This causes the binding energy of the daughter nucleus to increase which essentially cancels out the -m_e c^2 from the emitted \beta particle.