I have a task where there is a uranium pellet (mass=10g) with 3.5% U-235 and 96.5% U-238. Now I should calculate how much mass the pellet loses. I shall only consider the decay of U-235 and consider that 0.27g of U-235 decayed.
U-235 gets split according to following formula:
U-235 + neutron -> 100Zr + 133Te + 3*neutrons
I now calculate the number of uranium atoms in those 0.27g
N=0.00027kg/m(U-235). Since the free neutrons decay on their own and should not contribute to the mass of the pellet I assume that the mass loss per split is
Δm = m(U-235) - m(Zr-100) - m(Te-133). Now I multiply that with the number of decays I calculated earlier and I should get the mass loss of the pellet. However, it seems as if the proposed solution of the tasks wants me to simply use the normal mass defect equation (using the neutrons). My teacher explained it confusingly, something about "since I also subtract the neutrons from the Uranium mass they are considered to be gone (what I wanted to achieve with my approach)". So it seems as if the correct mass loss would be
Δm = m(U-235) - m(Zr-100) - m(Te-133) - 2*m(neutron).
I don't understand that, since that mass difference Δm would be tinier as the one I calculated earlier. And shouldn't it be bigger since neutrons are missing? Or am I overthinking this and ignore that neutrons decay - since they decay into a proton, which effectively has almost the same mass as a neutron, so their mass still contributes to the mass of the pellet?