Mass-energy conservation in nuclear reactions

AI Thread Summary
The discussion focuses on the conservation of mass-energy in nuclear reactions, highlighting a mistake in applying these principles. The participant calculated the total mass of reactants and products but arrived at an incorrect energy result, suggesting a need to consider the energy of the alpha particle. Key relationships between initial and final rest masses and kinetic energies are emphasized to clarify the conservation principle. The importance of showing detailed calculations is noted to identify potential errors. Understanding the mass-energy relationship is crucial for solving the problem correctly.
voreryar
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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
viber_image_2023-05-29_16-46-06-465.jpg

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
 
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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?
 
Can you show your work?
 
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?
 
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