Neutrons attach to atomic nuclei and transform them into other elements by literally slamming into the nucleus. It's not really about convenience, even a 0.00001% chance of a neutron hitting an atom just right to transform it is inevitable when we talk about the number of atoms in a given volume. The molar mass for atmospheric oxygen (2 oxygen atoms) is about 32 grams. 6 x 10^23 molecules of O2 weighs 32 grams. There's a lot of atoms around a nuclear explosion taking place on earth.

Any atom can be radioactive, they do not need to be heavy. Tritium for example is a radioactive form of hydrogen with 2 neutrons. Hydrogen is stable and not radioactive with 1 or 2 neutrons. There's generally a ratio between neutrons and protons (really simplifying this) where elements tend to be stable. Go outside of that ratio and the element tends to be unstable and will decay into something else. The why is related to quantum mechanics.