why does splitting a nucleus create a tremendous amount of energy?

Answer 1

This is only true for very heavy nuclei. When very heavy nuclei are split, the pieces that are left have less total mass than the original nucleus. The lost mass m is converted to energy according to Einstein's formula
E = m c^2

Just why heavy nuclei have more mass per nucleon is "explained" by the Curve of Binding Energy, which can be derived from quantum chromodynamics, but this theory is very difficult to apply mathematically.