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Is there any sort of sequence in the emission of radioactive particles? ie. alpha, beta, gamma or any other type of decay I don't know about.

Specifically, I wanted to know is there any evidence to support the fact that there is a gamma decay immediately after a beta-particle decay? And if so, is there any reason for this? And also, is the energy of every gamma decay the same?

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First, while $\beta $ particles were identified early in the study of radioactive decay, the classic $\beta $ particle is a high-energy electron, part of $\beta $ - decay. Such an electron does not usually produce $\gamma $ radiation.

On the other hand, $\beta $ + decay produces a positron, and this will quickly encounter an electron, the two will annihilate, and a pair of 511 keV photons will be produced. And yes, 511 keV is $\gamma $ radiation.

As to your larger question, the answer is, "sort of, but not really". Generally speaking, $\gamma $ radiation is at the end of many decay chains, so you can sort of consider it the last in the sequence, except that electron/positron pair production occurs when a 1.022 MeV + photon hits an atom, so there's no absolute rule.

$\alpha $ (helium nuclei) and $\beta $ (electrons or positrons) processes are not ordinarily sequential, so it's not appropriate to talk about one occurring before the other.

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