# Mass-energy conservation in nuclear reactions

• voreryar
In summary, the conversation discusses a problem involving conservation of mass-energy, where the total mass of the products is greater than the total mass of the reactants. The person is trying to find the correct answer using the formula E=mc^2 and converting from Joules to eV, but their answer is incorrect. They are advised to show their work and consider the energy of the alpha-particle given in the question.
voreryar
Homework Statement
If the energy of the incident alpha-particle is 7.68 MeV, calculate the kinetic energy of the proton assuming it gets 17/18 of the available kinetic energy
Relevant Equations
E = mc^2

I found the total mass of the reactants and the products, found the change in mass, used E=mc^2 and changed my answer from Joules to eV, but my answer is wrong. I'm guessing I have to do something with the energy of the alpha-particle given in the question

The answer is supposed to be: 6.58 MeV

Did you notice that the total mass of the products is greater than the total mass of the reactants? How do you account for this?

voreryar said:
I found the total mass of the reactants and the products, found the change in mass, used E=mc^2 and changed my answer from Joules to eV, but my answer is wrong.
Hi @voreryar. Welcome to PF.

You need to show your working so we can spot any mistakes you have made. But it sounds like you haven’t applied conservation of mass-energy correctly.

voreryar said:
I'm guessing I have to do something with the energy of the alpha-particle given in the question
Good guess!
Initial total rest mass ##=m_i##.
Final total rest mass ##= m_f##.
Initial total kinetic energy of all particles ##= K_i##.
Final total kinetic energy of all particles ##= K_f##.

What is the relationship between ##m_i, m_f, K_i## and ##K_f## in this problem?

## What is mass-energy conservation in nuclear reactions?

Mass-energy conservation in nuclear reactions refers to the principle that the total mass and energy in a closed system remain constant before and after a nuclear reaction. This principle is derived from Einstein's equation E=mc², which states that mass can be converted into energy and vice versa.

## How does mass-energy conservation apply to nuclear fission?

In nuclear fission, a heavy nucleus splits into smaller nuclei along with the release of energy. The total mass of the resulting particles is slightly less than the original mass of the heavy nucleus. The "missing" mass has been converted into energy, demonstrating mass-energy conservation.

## What role does mass-energy conservation play in nuclear fusion?

In nuclear fusion, light nuclei combine to form a heavier nucleus, releasing energy in the process. The mass of the resulting nucleus is slightly less than the sum of the masses of the original nuclei. This mass difference is converted into energy, consistent with the principle of mass-energy conservation.

## Can mass-energy conservation explain the energy released in nuclear reactions?

Yes, mass-energy conservation explains the energy released in nuclear reactions. The difference in mass between the reactants and products is converted into energy according to E=mc². This energy is what powers nuclear reactors and atomic bombs.

## What are some practical implications of mass-energy conservation in nuclear reactions?

The practical implications include the ability to harness nuclear energy for electricity generation in nuclear power plants, understanding the processes powering the sun and other stars, and the development of nuclear weapons. It also has implications for radiation therapy in medicine and various scientific research applications.

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