# Alpha decay and conservation of energy

I understand how alpha decay works but while reading through the text I came across this "All the emitted alpha particles travelled at the same speed, meaning they had the same amount of energy". How does the speed relate to the overall energy and they use the word particles so can multiple alpha particles be released at once?

There is only one alpha particle per decay. They're referring to multiple examples of the same isotope undergoing alpha decay.

The speeds are all the same because of conservation of mass-energy. Changing the speed would change the kinetic energy, and there is no other parameter in the final state that can vary to make up for that and keep conservation of mass-energy balanced.

The parent nucleus decays to an alpha and a daughter nucleus and the difference in energy $E$ is converted to kinetic energy of the two. However momentum is also conserved so they have equal and opposite momentum, meaning that the energy of the alpha is completely specified (non-relativistically, ${p^2\over 2m_\alpha}+{p^2\over 2 M_{daughter}}=E$). So all alpha particles from such a decay have the same energy and the same velocity (which means the same range, which is usually what you see).

The reason for pointing this out is to contrast it with $\beta$ decay, where the parent decays to a daughter, an electron (beta particle) and a neutrino, and the energy can be shared between the three in a range of ways that still conserve energy and momentum, so beta particles have a continuous energy spectrum..

BTW if there is a more politically correct terminology than parent-daughter I apologise for not knowing it.

The decay scheme for Po-210 is shown below.

What you will noice is that alpha particles with two different energies are emitted but each of the two different transitions produce alpha particles all of the same energy (and hence speed), either 4.502 MeV or 5.305 MeV.
Only one alpha particle is produced from the decay of a single Po-210 nucleus.

I think that the statement which is made about monoenergetic alphas is to contrast the single valued energy of alphas with the energies of the emitted beta particles which have a range of values due to emission of an anti neutrino at the same time.