A certain book I read says this
Scientist have found the weight of each particle,a neutron,proton,electron
So they can find the mass of each atom's nucleus.
But the odd thing was the nucleus in all atoms except for hydrogen had a certain small amount of mass "missing" from what it "should" be.
And to them this was not right.
Unrelated to the above,
at that time they had a law called the
Law of conservation of energy-which said energy can neither be created nor can it be destroyed but only changed from one from to another.
Their law was almost correct which in science,where there is no almost,is to say that they were wrong.
For the scientists of that age also had another law the law of conservation of mass.
They thought that energy and mass are two completely different things,they could not understand why energy sometimes acted like mass and why mass sometimes acted like energy.
Then somebody came around and wrote:E=mc^2
A simple sentence in the language of maths.
so.....lets go back to the unrelated problem of our nuclei missing mass....
every atom that had more than 1 proton was missing mass.
they concluded that "somehow" the nucleus had converted some of its own mass into energy,energy which it used to keep its self together.
And so atomic energy was created and the atomic age began.
(I wrote all of this from the book as far as I could remember it)