What does nuclear energy have to do with this splitting process?"
First of all, let's find out what is the total mass of the nuclei before and after the fission. Since the dimensions of the nuclei are so microscopic, let's now imagine ourselves to be reduced to the size of the order 10-14 m. Then, we can see clearly what's going on in the nucleus.

Change in mass during nuclear fission

One typical nuclear fission: U + n --> Nd + Kr + 2 n
The animation includes the weighing of U-235, a neutron, Nd and Kr.
Mass in nuclear physics is measured in unified atomic mass units (u), with
1u = 1/12 of the mass of the carbon-12 atom, that is, 1.66 x 10-27kg.
Total mass before the reaction ( mass of U-235 + n)
= 235.0439u + 1.0087u
= 236.0526u
Total mass after the reaction ( mass of Nd + Kr + 2n)
= 147.9169u + 85.9106u + 2 x 1.0087u
= 235.8449u
There is a decrease in mass by 0.2077u. This mass has been converted to energy, known as nuclear energy.)

In 1905, while Einstein was developing his special theory of relativity, he made the startling suggestion that energy and mass are equivalent!

He predicted that if the change in mass of a body is m, the energy of the body will change by E where E = mc2 , c is the speed of light 3 x 108 ms-1

Therefore, any reaction that produces an appreciable mass decrease is a possible source of energy. That's why nuclear fission is an important process in generating nuclear power.

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