Why does it take less binding force to hold the two atoms that a uranium atom has split into? When a Uranium atom splits into two there is a little bit of mass left that is equivalent to a big amount of energy (e=mc^2) and it explodes in fission 
It takes less binding force to keep the two atoms together than it does with the original atom
Why?
 A: There is a really helpful page about binding energy here:
https://courses.lumenlearning.com/physics/chapter/31-6-binding-energy/
In particular, if you see the chart of binding energy per nucleon you see that generally binding energy should increase proportionally to the number of nucleons.

When fission occurs, it splits into two or three fission fragments typically, these are your resultant elements that you are talking about.  However, neutrons, protons, electrons, and a bunch of other particles have a probability of being released due to this fission event.  These reduce the overall number of 'nucleons' in the resulting fission fragments.  Additionally, after fission, every object is moving apart with some kinetic energy.
In short, the binding force is proportional to number of nucleons, but all nucleons in the original atom won't be rebound in the fragments.
A: 
Now lets look at fission. An example of fission is when a Uranium-235 atom is split by a neutron into a Barium-144 atom, a Krypton-89 atom and three neutrons. Now looking at the graph the binding energy per nucleon for Uranium is about 7.6MeV and for Barium around 8.3 giving an increase in binding energy during fission of about 0.7MeV per nucleon, or a total of 164.5MeV in total. 
The appearance of extra neutrons is crucial to the matter of nuclear energy,   As you go to heavier and heavier nuclei in the nuclear table the number of neutrons relative to protons gets larger and larger. Therefore if a heavy nucleus like uranium splits into two medium-sized nuclei, there are too many neutrons around to fit comfortably on those two nuclei. Hence there are always a few leftover neutrons.
The two nuclei fly apart very rapidly. Energy is available because the total mass on the right side is less than that on the left. Although the number of protons and neutrons are the same, the krypton and barium nuclei are more tightly bound than the uranium; their binding energy is greater. 
