# Why do $\beta$ particles not get attracted to the nucleus?

I currently have a very limited knowledge of how radiation works etc, but while sat in class the other day, one question occurred to me that even my teacher could not answer.

We have been learning about alpha, beta and gamma radiation. I know that alpha is positive and that makes perfect sense. However, when the neutron is broken down to form a β particle and this particle is then sent out of the nucleus, why is this negatively charged β particle not attracted (presumably by electromagnetic force) back into the overall positive nucleus of the atom? To me, at least, it does not make sense that it would not be attracted back the nucleus.

Sorry if this is simple stuff but even after some furious googling I haven't been able to find an answer.

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A $\beta$ particle (an electron) is emitted with a very high energy, more than enough to overcome the potential and escape the nucleus. Also, an electron anti-neutrino is emitted which carries away a lot of the energy freed up in the decay so even if the electron were pulled back to the nucleus there wouldn't be enough energy available to reverse the process (electron capture). – Brandon Enright Jun 9 '14 at 16:15
@BrandonEnright: I think that's an answer. – JamalS Jun 9 '14 at 16:18

## 2 Answers

Simply put, the electron is going too fast. The nucleus will indeed attract it and this will slow down the β particle, but this is not enough to recapture it.

To put some numbers in, beta decay energies range from a few keV to a few tens of MeV; this is much more than the few tens of eV that are typical of atomic bound states. It is only the inner shells of heavy atoms that can go into the keV regime, but those are already full so the beta cannot be captured there.

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If you think about it, a beta particle is an electron (or positron) moving with high energy (which translates to high velocity due to the low mass). The coulomb attraction between the nucleons and the electron is strong, but not sufficiently strong to change the trajectory of the beta particle such that it's reabsorbed by the nucleus - it may simply change the trajectory without recapture.

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