Physics Narrative for 14-16
Emission can change elements
One of the most fundamental principles in the universe is the conservation of charge. You may have already met it, albeit implicitly, in the SPT: Electric circuits topic. The charge does not get lost as the charged particles drift round the loop. Look at any section of loop over time and the number of charged particles entering will be the same as that leaving: you cannot manufacture charge. At the nuclear level the same rule applies. So, when a nucleus emits a charged particle, we ought to expect some corresponding change in the nucleus.
If a positively charged particle is emitted from the nucleus, then the charge on the nucleus is reduced: if a negatively charged particle is emitted, then the charge on the nucleus is augmented. The charge (of the nucleus and emitted ionising particle) before the emission is the same as the charge (of the nucleus and emitted ionising particle) after the emission. As the remaining atom will, after a short interval, be neutral again, you might also expect the number of atomic electrons to change as a result of the nuclear change. So the chemistry will change, as this depends, in turn, on the number of atomic electrons. The atom is now a new element, with new behaviours and a new structure.
Emission of gamma radiation does not result in transmutation, as there is no change in the charge of the nucleus, so there is no need for a gaining or shedding of one or more atomic electrons to achieve a neutral atom.
Stability depends on the nuclear store, which depends on the arrangement of neutrons and protons
The number of protons in the nucleus sets the element: the number of neutrons affects the stability. This is not too surprising: if you tried to cram lots of positively charged particles together, without any nuclear glue, you'd expect the resulting electrical forces to make the nucleus rather unstable.
Moves towards a more stable, lower energy system result in a number of different emissions, depending on the nucleus. There are huge numbers of possible nuclei, constructed from selected numbers of neutrons and protons, and only a few are truly stable. Some are very unstable, perhaps even decaying so rapidly that you'd have a real difficulty in convincing yourself that you'd actually managed to make anything. The more unstable, the greater the fraction that decays in each interval of time (picoseconds to teraseconds), and so the shorter the half-life. A number of the more common emissions are given here, but you can see from the graphic that there are many, many more. In each case there is movement towards a more stable, lower-energy state, where the nucleons are more tightly glued together afterwards.
How well glued together the nucleons are can be measured by the energy that you'd need to provide to release each nucleon: this is the binding energy per nucleon. Energy is shifted from the nuclear store as more stable nuclei are formed: there is less energy in the nuclear store after the change and this energy turns up elsewhere.