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!!! :)
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!!! :)
-
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).
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).