# Available energy in β+ and β- nuclear reaction

duchuy
Homework Statement:
Formula demonstration
Relevant Equations:
Ed = [Mn(X) – (Mn(Y) + m(e))] c2
Hi,
I understood that to calculate the available energy in these two reactions could be calculated from Ed = [Mn(X) – (Mn(Y) + m(e))] c^2, but when I have to change use the atoms' mass instead of the nucleons' mass, it gives out two different formulas :
Ed = [M(X) – M (Y)] c2 for β-
Ed = [M(X) – (M(Y) + 2 m(e))].c2 for Ed = [M(X) – (M(Y) + 2 m(e))].c2 for β+
Can someone please explain to me why for β-, the mass of the electron isn't taken into consideration whilst for β+, we'd have to add the mass of two electrons ( when we are using the mass of the atom to calculate ).
Sorry if I have misused any vocabulary, I translated this from french.
Thank you so much for your help!

duchuy
Please be more specific. What does Ed represent? What two reactions is Ed associated with?
I'm so sorry for that.
Ed represents the available energy. The formula Ed = [Mn(X) – (Mn(Y) + m(e))] c2 uses the mass of the entire atom and is used for β+ and - reaction.
But when only the mass of the nuclei are given, we end up with two different formulas :
Ed = [M(X) – M (Y)] c2 for β-
Ed = [M(X) – (M(Y) + 2 m(e))].c2 for Ed = [M(X) – (M(Y) + 2 m(e))].c2 for β+
I just don't understand what happened to the mass of the electrons in these two reactions.
Thank you!

Homework Helper
Gold Member
Ed represents the available energy.
The available energy when what happens?

duchuy
The available energy when what happens?
I think it's the available energy in an atom with either an excess of neutron or proton depending on the β radioactivity. I'm not quite sure though sorry, it's just what's written in the text that we have to learn...

duchuy
I think that the prof doesn't like negative signs, so instead of using the energy released which is going to have a negative value when we consider the system, he just uses the available energy so the energy would be positive. I didn't get the chance to ask him since all classes are uploaded videos...