Force balances, baby!
The nuclear force (very strong) holds the nucleus of atoms together. The electrical force (less strong) pushes all the protons in the nucleus apart. The two forces battle it out, but usually nuclear wins and the atom stays together.
At some point when the nucleus gets big enough, electrical forces (which act over a long distance) overpower the nuclear forces (which act only on short distances). Then you can sort of tap the nucleus (with a “slow neutron”) and the whole thing blows apart.
Basically: they understood force balances.
Source: I’m an applied mathematician and lots of physics based math comes down to force balances
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