Lol Dumbledore, bit dodgy there.. You fed some incorrect + irrelevant info and didn't answer the dotpoint.. You barely described Fermi's inital observation, you led on to some random stuff and the dotpoint asked for nuclear fission. Fission is the splitting of an atom into two smaller atoms, not beta decay.
Fermi's initial experimental observation was the Uranium bombardment, the pile he built in his university is a different dotpoint.
Fermi bombarded lots of things with Neutrons and one day he had the idea of bombarding a Uranium-238 atom. When he did so, he noticed that the resulting matter had less mass than the original matter! He didn't know exactly what he was seeing and thought that the Uranium-239 was becoming Plutonium-239, which was partially true. It was later realised that the missing mass (now called mass defect) had turned into energy, by Einstein's equation e=mc^2.
What was actually happening was that the Uranium-238 atom absorbed the neutron becoming Uranium-239. This is an unstable isotope and it underwent beta decay into Neptunium-239 and another beta decay into Plutonium-239. It then underwent nuclear fission into smaller atoms, such as Barium and Krypton. It is important to note that Fermi initially didn't know he was observing fission, and that when he repeated his experiment, different levels of energy were being detected. This is because when Uranium-239 undergoes fission, it can split into different pairs of elements.
Btw that's from memory so don't blame me if I'm wrong