What happens to unstable nuclei over time?

They typically decay via fission (the splitting of a nucleus) to form a pair of daughter nuclei. Different unstable nuclei decay via different processes, such as alpha decay or beta decay.

for example Polonium-210 undergoes alpha decay to form the stable isotope Lead 206.

If the daughter nuclei are themselves unstable, they will also undergo radioactive decay until all nuclei are stable.

Nuclear fission happens at random- there is no way of predicting when or if a particular nucleus will decay, however for very large numbers of nuclei the half-life can be measured. Half life is the amount of time it takes half of the nuclei in a sample to decay and can range from incredibly short, on the order of 10^-24 seconds for Hydrogen-7, to very long, on the order of 10^30 seconds for Tellurium-128. This is over 160 trillion times the age of the universe!