# Variation in mass and binding energy in nuclear reactions

• Krushnaraj Pandya
In summary, the two statements are correct, but the sign convention for binding energy is unfortunate.
Krushnaraj Pandya
Gold Member

## Homework Statement

I'm perpetually confused keeping track of the energetics of a nuclear reaction and I broke down my conceptual questions into the following parts
statement a-In a fission reaction, the two medium sized daughter nuclei each have more binding energy per nucleon than the original nucleus
statement b-In a fusion reaction the heavier nucleus has more binding energy per nucleon than the lighter ones

Which of these statements are correct and why, I know that mass of the reactants is always higher (the loss in mass is released as energy) and total binding energy of reactants is always lower (I can't visualize this very well) for a spontaneous reaction but I can't figure out the validity of the above statements and I'd really appreciate some help with that-thank you.

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## The Attempt at a Solution

Mentioned above

Both statements are correct for reactions that release energy. There are also reactions that do not. You can e.g. fuse heavy nuclei with an accelerator delivering the necessary energy.
Krushnaraj Pandya said:
and total binding energy of reactants is always lower (I can't visualize this very well)
The sign convention for binding energy is a bit unfortunate.

If in doubt you can always consider the total energy.

mfb said:
Both statements are correct for reactions that release energy. There are also reactions that do not. You can e.g. fuse heavy nuclei with an accelerator delivering the necessary energy.The sign convention for binding energy is a bit unfortunate.

If in doubt you can always consider the total energy.
How can we use total energy without using the sign convention for binding energy?

Do you mean to say we'd use rest mass*c^2 of reactants+ KE due to any velocity =rest mass of products*c^2 +KE

That always works, sure.

mfb said:
That always works, sure.
Alright, thank you very much :D

## 1. What is the relationship between mass and binding energy in nuclear reactions?

The relationship between mass and binding energy in nuclear reactions is described by Einstein's famous equation, E=mc². This equation states that mass and energy are interchangeable, meaning that any change in mass will result in a change in energy.

## 2. How does variation in mass affect the stability of a nucleus?

The stability of a nucleus is directly related to its binding energy. A higher binding energy means that the nucleus is more stable, while a lower binding energy indicates a less stable nucleus. Therefore, any variation in the mass of a nucleus will also affect its stability.

## 3. Can changes in binding energy lead to different types of nuclear reactions?

Yes, changes in binding energy can lead to different types of nuclear reactions. For example, when a nucleus with a high binding energy splits into two smaller nuclei with lower binding energies, this is known as nuclear fission. On the other hand, when two smaller nuclei combine to form a larger nucleus with a higher binding energy, this is called nuclear fusion.

## 4. How does the binding energy per nucleon vary across different elements?

The binding energy per nucleon varies across different elements. Generally, larger elements have a higher binding energy per nucleon compared to smaller elements. This is because larger nuclei have more nucleons, which means a stronger nuclear force is needed to hold them together.

## 5. Are there any practical applications of understanding variation in mass and binding energy in nuclear reactions?

Yes, there are many practical applications of understanding variation in mass and binding energy in nuclear reactions. This knowledge is essential for nuclear power plants, as it helps scientists and engineers understand how to control nuclear reactions for energy production. It also plays a crucial role in the development of nuclear weapons and in studying the origins of the universe through nuclear astrophysics.

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