Available energy in β+ and β- nuclear reaction

• duchuy
In summary, the two formulas for Ed represent the available energy in two different radioactivity states.
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!

kuruman said:
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!

duchuy said:
Ed represents the available energy.
The available energy when what happens?

kuruman said:
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...

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...

What is the difference between β+ and β- nuclear reactions?

β+ and β- nuclear reactions are both types of radioactive decay, where an unstable nucleus emits a beta particle (either a positron for β+ or an electron for β-) in order to become more stable. The main difference between the two is that in β+ decay, a proton in the nucleus is converted into a neutron, while in β- decay, a neutron is converted into a proton.

How is available energy calculated in β+ and β- nuclear reactions?

The available energy in a β+ or β- nuclear reaction is calculated using the mass-energy equivalence formula, E=mc^2. This formula takes into account the difference in mass between the parent nucleus and the resulting daughter nucleus, which is converted into energy during the decay process.

What factors affect the amount of available energy in a β+ or β- nuclear reaction?

The amount of available energy in a β+ or β- nuclear reaction is affected by several factors, including the mass difference between the parent and daughter nuclei, the stability of the resulting daughter nucleus, and the type of beta decay (β+ or β-) that is occurring. Additionally, the nuclear binding energy of the parent and daughter nuclei also plays a role in determining the available energy.

How does the available energy in a β+ or β- nuclear reaction impact the decay rate?

The available energy in a β+ or β- nuclear reaction does not directly impact the decay rate. However, it can indirectly affect the decay rate by influencing the stability of the resulting daughter nucleus. If the available energy is high enough, the daughter nucleus may be more stable and therefore decay at a slower rate.

What are some practical applications of β+ and β- nuclear reactions?

β+ and β- nuclear reactions have several practical applications, including medical imaging and cancer treatment. In medical imaging, radioactive isotopes that undergo β+ or β- decay are used to create images of the body's internal structures. In cancer treatment, high-energy β- particles are used to destroy cancer cells. Additionally, β+ and β- decay can also be used in power generation and industrial processes.

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