# Is an atom charged after undergoing beta emission?

After beta emission, an atom's mass number remains the same while the number of protons increases by one. As far as I know, the beta particle (electron) is too energetic to be recaptured.

If this is true, is an atom charged after undergoing beta emission (since the electron number is unchanged and the number of protons has increased by one)?

• related: physics.stackexchange.com/questions/146549/… . Note that there are two types of beta decay. You seem to be referring to $\beta^-$ decay. the electron number is unchanged This is probably not true. Beta decay is a violent process, so other electrons are likely to be knocked out. – user4552 Nov 19 '14 at 16:51

Most atoms have an ionization energy of a few tens of electron volts. Beta decay electrons typically have a range of energies, with the mean and maximum energies typically a few million electron volts; the probability that the electron energy is small enough to be captured is pretty small.

In addition, the daughter atom cannot capture the decay electron unless there is a spot in the daughter atom for the electron to live. The daughter atom must have an unoccupied $s$-wave electron orbital, since the wavefunctions for the $p$-wave, $d$-wave, etc. orbitals all have a zero at the nucleus. Furthermore, of the $s$-wave wavefunctions, only the $K$-shell (innermost) actually has a maximum within the nucleus; all the wavefunctions with higher principal quantum number will have reduced overlap with the beta decay electron, and therefore reduced probability for the decay electron to appear in the bound state.

These considerations make the most likely candidates for beta decay to a neutral atom limited to the two nuclides with a vacancy in the $1s$ electron shell: \begin{align} \mathrm n &\to \mathrm H + \bar\nu_\mathrm e\\ {}^3\mathrm H &\to {}^3\mathrm{He} + \bar\nu_\mathrm e \end{align} I don't believe either has actually been observed. There is a current experiment searching for the neutron decay to neutral hydrogen.

So, the answer to your question is yes: an atom is usually charged after a decay, and beta decay to a neutral daughter atom is a rare and interesting occurrence. Most likely is that the daughter atom will have charge $+1$ as the fast electron departs; it is even possible for the beta electron to knock bound electrons free of the nucleus, leaving the daughter in higher charge states and emitting X-rays as the ion cools down.

Yes, the atom (along with the surrounding material) may have a lasting electron deficit after the beta particle emission because harvesting this surplus charge is how betavoltaics work.

Beta particles are more penetrating than charged nuclei like alpha particles, and because of that I believe they are better at carrying the charge away. The exact reasons for this are complicated, but the beta particle (electron) travels at very high speeds due to lots of energy from the nuclear decay being deposited into such a small mass, and they are often fully relativistic. Emission of heavy charged particles can still carry away charge from the material, but it would require a thin sheet like in the Rutherford gold foil experiment.

• the Betavoltaic device Wikipedia page says "converting the electron-hole pairs produced by the ionization trail of beta particles traversing a semiconductor.", so one exploits the many electron-hole pairs which are created and not just the single beta electron and vs. the hole in the decayed atom. – Andre Holzner Mar 17 '16 at 10:40

Yes. After beta decay the atom has charge +1. Electron has energy about 1MeV but due to scattering on the another atoms lose energy and stop.

• Thank you. Do you have any sources? – Soham Chowdhury Nov 19 '14 at 21:43
• See Krane (Intro. Nuclear Physics) or Yang and Hamilton (Modern Atomic and Nuclear Physics). – Bill N Jan 21 '15 at 21:22

Just learned this in my chemistry class

Okay After beta decay one neutron from the nuclei is "converted" into a proton giving the atom a +1 charge therefore positively charging the atom. Not going to go into the complex electron and an antineutrino creation.

Since Beta decay is one process that unstable atoms can use to become more stables beta decay moves the atom's ratio of protons and neutrons to a more optimal/stable ratio of protons and neutrons

It really does depend on what type of beta decay your talking about because there two different types - beta minus and beta plus

Beta minus (β−) decay produces an electron and electron antineutrino

beta plus (β+) decay produces a positron and electron neutrino

basicly in terms of protons beta minus and plus are opposites because in beta minus a neutron turns into a proton and vice versa.

Sources:

https://en.wikipedia.org/wiki/Beta_decay