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

[From: ] [author: ] [Date: 12-06-11] [Hit: ]
014102u, proton = 1.ANS: energy of products = 1.how do you get energy of products? i dont understand.why cant i get the answer by taking (mass of X + mass of proton)(u)c^2?......
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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The mass of Y + deuteron = 54.938047 + 2.014102 = 56.952149 u

The mass of X + proton = 55.938906 + 1.007825 = 56.946731 u

You will note that the mass has reduced slightly during the reaction. This is because the mass has been turned to energy (according to E=mc²). It is this ;'converted' mass, plus the initial kinetic energy, that equals the released energy.

Mass loss = 56.952149 - 56.946731= 0.005417u
1u = 1.66053886*10^-27 kg.
Mass loss = 1.66053886*10^-27 x 0.005417 kg = 8.995x10^-30 kg

This mass is converted to energy: E = mc² = 8.995x10^-30 x (3x10^8)²
= 8.0955x10^-13J

This would be the amount of energy released is the deuteron started with no kinetic energy. But the deuteron had a kinetic energy of 2.1MeV, which is 2.1x10^6 x 1.6x10^-19 J = 3.36x10^-13J.

Since total energy is conserved, to calculate the correct energy release 3.36x10^-13J. must be added to 8.0955x10^-13J giving
3.36x10^-13 + 8.0955x10^-13 = 1.1146x10^-12 J, which is the required answer (ignoring rounding error).
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