How is overall charge neutrality conserved in beta decay?

[Andy Resnick]

This is probably a dumb question, but a student asked me and I can't figure out the answer:

When a nucleus decays via beta decay, for example (in poorly formatted text):

55 Cs → 56 Ba + e− + ν

How is overall charge neutrality conserved? Clearly, the reaction appears to conserve charge, but if we start with a neutral Cs atom (55 electrons), the resultant Ba atom is now a positive ion (56 p+, 55 e-).

Is this what happens? Does the radioactive material slowly shed negative charge and accumulate excess positive charge? I understand there is an electron capture reaction (which does not apply here), and I suspect the nuclear decay is violent enough that orbiting electrons are perturbed, but I honestly don't know how to answer the question.

Thanks in advance.

 

[SpectraCat]

This is probably a dumb question, but a student asked me and I can't figure out the answer:

When a nucleus decays via beta decay, for example (in poorly formatted text):

55 Cs → 56 Ba + e− + ν

How is overall charge neutrality conserved? Clearly, the reaction appears to conserve charge, but if we start with a neutral Cs atom (55 electrons), the resultant Ba atom is now a positive ion (56 p+, 55 e-).

Is this what happens? Does the radioactive material slowly shed negative charge and accumulate excess positive charge? I understand there is an electron capture reaction (which does not apply here), and I suspect the nuclear decay is violent enough that orbiting electrons are perturbed, but I honestly don't know how to answer the question.

Thanks in advance.

I asked the same question in my nuclear physics class, and although I can't recall the precise answer (it was a long time ago), this was the general idea.

Since charge is conserved in the reaction, you haven't really created any new charged particles. You have instead created an electron-hole pair, in much the same way as you might do by shining light on a semi-conductor. Eventually, the electron will re-combine with the hole, although this may take a while and occur through several steps.

For example, let's assume that the Cs atom is embedded in some bulk material. The beta-electron will be emitted and travel some distance away into the bulk material as an exciton. The Ba ion "hole" created might then "capture" (not the nuclear decay process, just charge recombination) an electron from an adjacent atom, resulting in "hopping" of the hole. Eventually the "hole" will recombine with the electron exciton.

The situation is different if the Cs atom is at the surface, and the electron is emitted (say) into the atmosphere. At that point, you do get a charge imbalance, but a small amount of charge imbalance is not a big deal for macroscopic systems. Unless the beta decay rate is extremely fast, the electrons can be replenished by small parasitic currents from "ground".

I suppose that if you had a well-isolated chunk of beta-active material in a vacuum chamber, you might eventually build up enough of a charge imbalance that the voltage would rise to such levels that you would get a spontaneous discharge, rebalancing the charge in spectacular fashion. I wonder if that has ever been observed?

 

[Drakkith]

How is overall charge neutrality conserved? Clearly, the reaction appears to conserve charge, but if we start with a neutral Cs atom (55 electrons), the resultant Ba atom is now a positive ion (56 p+, 55 e-).

It looks like you are neglecting to account for the electron created in the process. This will not be captured by the atom, so it will still be positively charged. Accounting for everything you will now have 56 protons and 56 electrons, only 55 of which are bound to the nucleus.Also, from wikipedia on conservation of charge:

This does not mean that individual positive and negative charges cannot be destroyed. Electric charge is carried by subatomic particles such as electrons and protons, which can be created and destroyed. In particle physics, charge conservation means that in elementary particle reactions that create charged particles, equal numbers of positive and negative particles are always created, keeping the net amount of charge unchanged. Similarly, when particles are destroyed, equal numbers of positive and negative charges are destroyed.

 

[Andy Resnick]

It looks like you are neglecting to account for the electron created in the process. This will not be captured by the atom, so it will still be positively charged. Accounting for everything you will now have 56 protons and 56 electrons, only 55 of which are bound to the nucleus.


Also, from wikipedia on conservation of charge:

I understand that. But the emitted electron is highly energetic and is not bound to the atom- is the daughter atom (in this case Ba) a positive ion? SpectraCat's response was more like what I was thinking- there is indeed a buildup of static charge which can be easily canceled by parasitic currents (even from the air). It's odd that the elementary textbooks are completely silent about this.

 

[Dadface]

Ba is a positive ion immediately after emission and in fact there will follow a line of positive ions and negative ions (electrons) caused by the beta particle ionising the atoms it collides with.The particles will quickly return to neutrality as positive and negative ions recombine.

 

[Drakkith]

I understand that. But the emitted electron is highly energetic and is not bound to the atom- is the daughter atom (in this case Ba) a positive ion? SpectraCat's response was more like what I was thinking- there is indeed a buildup of static charge which can be easily canceled by parasitic currents (even from the air). It's odd that the elementary textbooks are completely silent about this.

Perhaps I misunderstood your question. If you were asking how a material stays neutral after beta decay, then yes, I would say that it captures electrons from the air or whatever material it is sitting on. I thought you were asking about charge conservation.