Beta Plus Decay: What's Left for the Electron?

[InkTide]

TL;DR Summary

Positron emission converts a proton to a neutron - what happens to the now excess electron in a previously neutral atom?

Specifically, this would be beta plus decay and not electron capture, and assumes an electrically neutral radionuclide. Since beta plus decay is the emission of a positron from the nucleus as a proton transmutes into a neutron, the resulting atom now has 1 less elementary charge than before, but no electrons have been consumed, yielding an electron without an orbital to occupy in addition to the daughter isotope, positron, and electron neutrino.

What happens to this excess electron? Is it just left floating around, or does it stick around long enough to convert the daughter isotope briefly to an isolated -1 anion? Does it interact with the electron cloud of the neutral daughter isotope to inherit or contribute to the recoil energy of the daughter atom? What are the odds that it gets annihilated by the outgoing positron, and if that's even possible, what would that look like to an observer?

 

[Drakkith]

yielding an electron without an orbital to occupy

This isn't true. The electron absolutely has an orbital to occupy. Atoms and molecules can hold onto more electrons than they have protons because of how electrons are spread out over space compared to the much more compact and focused positive charge of the nucleus. That is, at close range, the positive charge of the nucleus isn't fully shielded by the electrons because they occupy a large volume compared to the nucleus. In fact, molecules in particular commonly have negative charges. Chlorate and perchlorate are examples of anions and there are many, many more.

What happens to this excess electron? Is it just left floating around, or does it stick around long enough to convert the daughter isotope briefly to an isolated -1 anion? Does it interact with the electron cloud of the neutral daughter isotope to inherit or contribute to the recoil energy of the daughter atom? What are the odds that it gets annihilated by the outgoing positron, and if that's even possible, what would that look like to an observer?

If the positron doesn't immediately annihilate with an electron, and if an electron or two isn't knocked out of the atom by the decay, then you'll end up with an atom with a -1 charge instead of being neutral. Unfortunately I don't know the odds of each of these happening or any real details of the process.

 

[InkTide]

Atoms and molecules can hold onto more electrons than they have protons because of how electrons are spread out over space compared to the much more compact and focused positive charge of the nucleus.

Very helpful, thank you.

an atom with a -1 charge instead of being neutral.

I guess the follow-on would be how long can the atom stay like that if it's in isolation? How quickly does the rest of the electron cloud shove the excess electron away, since we don't see many single atoms with -1 charge, as far as I'm aware? In more mathematical terms, I guess I'm wondering if the timescales and forces involved are going to impact what the decay looks like in isolation, especially in terms of the recoil energy. I'd expect if the daughter nuclide had very different electrical properties to the parent (e.g. Sodium-22 to Neon-22) the effect might be different as well.

 

[Drakkith]

I guess the follow-on would be how long can the atom stay like that if it's in isolation? How quickly does the rest of the electron cloud shove the excess electron away, since we don't see many single atoms with -1 charge, as far as I'm aware?

That's a good question and some quick searching led me to a term called electron 'autodetachment'. Apparently anions in an excited state can transfer energy to an electron as they undergo electronic transitions to their ground state that end up kicking the excess electron out. Which makes me curious as to how often you find a molecule or atom anion in its 'ground state' (minimum energy levels, but with -1 charge). We know anions exist, and we know that molecules are not always in their ground states and are often vibrating back and forth at room temperature, so would those molecules remain anions if allowed to lose energy and transition to a 'ground state'?

 

[mfb]

Almost every element in isolation can have an extra electron bound to it, with the noble gases as most relevant exception (Wikipedia has a table, look for negative values for exceptions). In matter things are more complicated and typically the extra electron will go elsewhere quickly. It's also possible that the recoil of the positron emission breaks some chemical bond the atom might have had.

 

[Vanadium 50]

First, the positron can go a good deal away from the parent atom. Depends on a lot of things, but I'd estimate mm-scale.

Second, I am a little surprised that noble gasses don't form negative ions, but only a little. To first order, recall that the H- ion is bound. Insofar as it can be considered a neutral hydrogen atom with an exttra electron, it doesn't matter if you replace the hydrogen atom by some other neutral atom.

This is an oversimplification, and one of the consequences seems to be that this model misses for a few percent or atoms - the noble gasses* - but it gives you an idea of why it might be so.

* I didn't look it up, but I wouldn't be shocked if the alkaline earth metals, at least some, were similar in this respect.

 

[mfb]

I see four groups:

* All noble gases: helium, neon, argon, krypton, xenon, radon
* The first two alkaline earth metals: beryllium, magnesium
* A couple beyond uranium: plutonium, berkelium, californium, einsteinium, nobelium, lawrencium
* Others: nitrogen, cadmium, zinc, manganese, mercury, ytterbium

 

[InkTide]

Ah okay, there's some periodic similarities there - looks like the f-block to d-block, d-block to p-block, and p-block to s-block transitions are disfavored. Notably, that's creating new types of orbitals. It's interesting that the only s-block to s-block jump that creates a new level of s-orbitals is also disfavored, but curious that s-block to f- or d-block are apparently just fine. Manganese and nitrogen don't make any sense to me, though I am a little suspicious of how consistently the actinides start hating electrons after plutonium. All of those sources list it as calculated or estimated for negative electron affinity, is there more recent experimental data? I'll have to read up on the model the calculations are using, since the calculations cited well predate much of our modern information on superheavy elements (literally every negative electron affinity besides Ytterbium in the chart is citing something from before 1990).

 

[snorkack]

Ah okay, there's some periodic similarities there - looks like the f-block to d-block, d-block to p-block, and p-block to s-block transitions are disfavored. Notably, that's creating new types of orbitals. It's interesting that the only s-block to s-block jump that creates a new level of s-orbitals is also disfavored, but curious that s-block to f- or d-block are apparently just fine. Manganese and nitrogen don't make any sense to me,

They do for me.
Look at patterns...
All noble gases - p⁶ to s¹;
The early alkaline earths - s² to p¹. Ca, Sr, Ba and Ra - to d¹ or f¹ are positive but pretty small
N is actually half-shell filling - p³ are filled with same spin electrons. P has positive electron affinity, but note how P also has affinity which is smaller than either Si or S either side.
Mn is also filling the d⁵ half-shell. I am unsure if the Tc estimate is actually correct, but Re has a conspicuous if positive minimum.
Zn, Cd and Hg are d¹⁰ to p¹ shell filling
Yb is f¹⁴ to d¹ shell filling.
It is the heavy actinides that look suspect.

though I am a little suspicious of how consistently the actinides start hating electrons after plutonium.