Decay never means disappear: problems with the dice analogy

It’s common in schools to model radioactive decay using a large number of dice. All the dice are thrown at once and the sixes are removed and put to one side. The process is repeated lots of times until all the dice have ’decayed’. This gives a nice feeling for exponential change since the fewer dice there are left the fewer sixes are thrown.

The problem with this analogy is with the removal of the dice. If you're not very careful it gives the impression that when a nucleus decays it disappears. This misconception even leaks into computer simulations. For example this very misleading simulation is in the top two Google results if you search for ’radioactive decay simulation’.

Nuclear decay happens when an unstable nucleus changes into a more stable form by emitting a particle. It never means the nucleus disappears. For example with alpha decay the nucleus gets smaller, with beta decay a neutron changes into a proton and with gamma decay the nucleus settles into a more stable ’shape’.

I've never come across a simulation (apart from with our Furry Elephant simulation of radioactive decay) where the emitted alpha or betas are actually shown. This is after all what you observe with your Geiger counter and there is a one-to-one relationship. Each decay gives rise to one particle.