Hideki Yukawa and the strong nuclear force
The existence of the nucleus alone did not explain why the nucleus doesn’t simply disintegrate from all the repulsive forces. The answer required as much imagination as every other concept in quantum physics. In the same year Chadwick received his Nobel Prize (1935), Hideki Yukawa calculated how much energy was required to keep a proton and a neutron bound to each other. Then, he imagined this energy coming from particles of a certain mass being transformed into energy (via E=mc2). But where was this mass coming from? Well, Heisenberg’s uncertainty principle proves mathematically that the law of conservation of mass can be broken for a sufficiently short amount of time—provided this “borrowed” mass is returned. So a particle can technically be created and destroyed (very quickly) without breaking any laws of physics, generating energy permanently. Therefore, the energy required to bind a proton and a neutron together is “virtual”—i.e. borrowed from the future and returned to nothingness. This concept was later known as the strong nuclear force. It was a very bold proposition by Yukawa; he calculated the mass of such a particle to be ~200 times heavier than the electron. Seemed impossible, but it was the only explanation anybody could come up with for the stability of the nucleus, and quantum theory supported it.
Source: "The Key to the Cosmos." Atom, presented by Jim Al-Khalili, season 1, episode 2, BBC Four, 2007
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Full disclosure, I may occasionally borrow a sentence from Will Durant's Story of Civilization. I absolutely love that collection!