Energy conservation in nuclear fission

[cormzy]

TL;DR

I know that in fission, a massive nucleus breaks up into two less massive nuclei, I know that the resulting nuclei have a greater binding energy per nucleon due to the decreased diameter of the nucleus which increases the strength of the strong nuclear force. (The strong nuclear force does work on the nucleus). I know that the mass defect is converted into kinetic energy of fission fragments.

Hi all,
I struggle to understand how energy is conserved I fission.
If the binding energy per nucleon increases, surely the mass defect simply accounts for that difference to conserve energy before and after.
How does the mass defect account for the kinetic energy of the fission fragments as well?

 

[Bandersnatch]

The difference in binding energy is the mass defect. It's not some separate effect that has to be accounted for.

Conservation of energy dictates that:
Mass of parent nucleus = mass of daughters + kinetic energy (and radiation etc.)
Where
mass = rest mass of components (same before and after) + (negative) binding energy
and
parent binding energy > sum of daughters binding energy (greater binding energy of daughter nuclei means it's more negative)
So
rest mass of components - rest mass of components + parent binding energy - daughters binding energy = kinetic energy
i.e.
$\Delta$binding energy (mass defect) = kinetic energy