How do you get the energy of products in nuclear reaction?

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SUMMARY

The discussion focuses on calculating the energy of products in a nuclear reaction involving the radionuclide X, produced by bombarding a stable isotope Y with deuterons. The reaction is represented as Y + deuteron -> X + proton, with a calculated energy release of 1.145 x 10^-12 J. Participants clarify that the total energy must account for both rest mass and kinetic energy, emphasizing the importance of conservation of total energy in nuclear reactions.

PREREQUISITES
  • Understanding of nuclear reactions and conservation of energy principles
  • Familiarity with atomic mass units (u) and their conversion to energy (E=mc²)
  • Knowledge of deuterons and their role in nuclear bombardment
  • Basic concepts of kinetic energy in particle physics
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  • Study the principles of conservation of energy in nuclear physics
  • Learn about the calculation of kinetic energy in particle collisions
  • Explore the concept of rest mass energy and its applications in nuclear reactions
  • Investigate the use of cyclotrons in producing radionuclides
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Students and professionals in nuclear physics, particle physicists, and anyone interested in understanding energy calculations in nuclear reactions.

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The radionuclide X has a half life of 2.58hours and is produced in a cyclotron at a constant rate by bombarding a Y target with 2.10 MeV deuterons. The target contains only the stable isoptope Y and the reaction that produces X is

Y + deuteron -> X + proton

show that energy is released in this reaction,
and hence calculate the energy of the products in the above reaction.

(atomic mass of Y = 54.938047u, X = 55.938906u, deuteron = 2.014102u, proton = 1.007825u)

ANS: energy of products = 1.145 x 10^-12 J

how do you get energy of products? i don't understand.

why can't i get the answer by taking (mass of X + mass of proton)(u)c^2?

thanks in advance! :)
 
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Welcome to PF:
You have a stationary target of Y with a moving d at the start, and a recoiled X with a moving p after.

You are not asked to work out how the energy of the products is distributed.
So you do 1. by comparing the masses before and after (remember the 2MeV incoming).

You do 2 by conservation of total energy.

why can't i get the answer by taking (mass of X + mass of proton)(u)c^2?
because that would be the rest-mass energy of the products ... you need their kinetic energies too.
 

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