Start a chain reaction, or introduce non-radioactive isotopes to prevent one. Control energy production in a nuclear reactor! (Previously part of the Nuclear Physics simulation - now there are separate Alpha Decay and Nuclear Fission sims.)
How did Rutherford figure out the structure of the atom without being able to see it? Simulate the famous experiment in which he disproved the Plum Pudding model of the atom by observing alpha particles bouncing off atoms and determining that they must have a small core.