During Beta decay experiments it was found that momentum and energy were not conserved as they should be. In Beta decay, a Neutron from the nucleus decays into a Proton and a high speed Electron (beta particle).
For example:-
Or more generally we can just consider the Neutron decaying to form a Proton and an Electron.
This decay should give an Electron of known Kinetic Energy, however, experimentally this is not the case:-