How come nuclei become more unstable the bigger they are?

The nucleus is made up of protons and nuetrons, which means there is an electric repulsion. The nucleus is held together by somethign called the strong nuclear force. This overrides the electromagnetic repulsion of the protons in the nucleus. However, the strong force only occurs at very small distances, so as the radius of the nucleus increases the electromagnetic force becomes greater and causes this instability.

Here I'd draw a graph with curves for the strong nuclear force and the electromagnetic force, with the positive side of the y axis showing repulsion and the negative showing attraction and then distance between protons as they x axis. The student should of seen this before, but I would point out where the point of equilibrium is and talk about the rates of increase and decrease in the gradient

So as the nucleus gets bigger the electrostatic force between protons that are further away will become greater than the strong force. This can cause alpha or beta decay, with alpha decay reducing the size of the nucleus (with two protons and two nuetrons being emitted) and beta decay changing the balance of the nucleus where a proton may turn into a nuetron (beta positive) or a nuetron may turn into a proton (beta minus decay).