Multiple choiceQuestion 1 · Recall
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By the end you can describe the shape of the alpha and beta energy spectra, explain why the alpha spectrum is discrete and the beta spectrum continuous, and say what the maximum beta energy represents.
Measure the kinetic energy of the particles emitted by a source and plot how many there are at each energy:
Alpha decay is a two-body process: the parent nucleus at rest becomes a daughter nucleus and an alpha particle. With only two bodies leaving, conservation of momentum fixes how the released energy must be split between them: they fly apart in opposite directions with equal and opposite momenta.
The split depends only on the two masses, so every alpha particle from that particular transition leaves with the same kinetic energy. A nuclide that can decay to more than one daughter state therefore shows a small number of lines, each corresponding to one transition.
There is no room for a range of energies in a two-body decay.
Beta decay is a three-body process: the daughter nucleus, the beta particle and an (anti)neutrino all leave.
Two particles plus a nucleus gives three bodies sharing one fixed amount of released energy, and momentum conservation no longer pins down a single split. On each decay the beta particle can take anything from almost none of the energy to almost all of it, with the (anti)neutrino taking the rest. Averaged over many decays, the beta particles show a continuous spectrum.
The maximum beta energy happens on the decays where the (anti)neutrino carries away almost no energy, so the beta particle takes essentially all the available energy. That end point is the same for every decay of that nuclide, which is why the curve always finishes at a definite energy rather than trailing off.
Think of the released energy as a fixed sum of money to be shared. In alpha decay there are exactly two recipients with a fixed deal between them, so each always gets the same amount.
In beta decay there are three recipients and no fixed deal, so the shares vary from decay to decay — but they always add up to the same total. The beta particle's energy is only one share, which is why it takes a range of values up to the whole sum.
This is also the historical argument for the neutrino: the missing energy had to be going somewhere.
Worked example: Reading a beta spectrum
The beta spectrum of a particular nuclide extends from 0 to 0.16 MeV. State the maximum kinetic energy a beta particle from this source can have, and explain your answer.