Why do some elements not have a stable isotope?


My (extremely limited) understanding of what causes an element to be either stable or reactive is due to a mismatch in energy in the nucleus due to either extra protons or extra neutrons. So why wouldn’t something like Plutonium-188 be stable, since it would have 94 protons and 94 neutrons?

In: 5

the nucleus is made of protons (with a positive charge) and neutrons (with no charge). because protons are all positive, they repel each other (remember that like charges repel), and they’re looking for any excuse to fly apart. that’s where the neutrons come in; they act as a sort of buffer between protons and hold the nucleus together. the force that is used to keep them together is called the strong nuclear force. as you add more protons, you get more interactions between them and a bigger chance of them flying apart, so you need more neutrons to fill in the space between them. for example, the most stable isotope of uranium is uranium-238, with 92 protons and 146 neutrons. at some point, there’s just no way to keep all the protons happy and they fly apart soon after being brought together.

you can kind of imagine the nucleus like a group of people that all really don’t like each other. in order to keep the group together, you need some mediators in between so that people don’t leave. with two or three uncooperative people, only a few mediators are needed, but as you add more and more people, more and more mediators are needed. sometimes, despite the mediators, people will still leave the group, and this is more likely the more people you have, and that’s how you get radioactive decay.

As mentioned, the basic parts of atomic nuclei are protons (p) and neutrons (n). There is something called the _(strong) nuclear force_ which is, as the name implies, rather strong, and it is also pretty weird. The important part is that it makes p and n behave similar to electric or magnetic poles: different ones attract, same ones repel each other.

So just a bunch of protons will not stick together, not even just two of them, unless there is at least one neutron “between” them. Indeed 2p+1n is Helium-3, which is stable.

If you have way more p than n, then it cannot hold together, the p’s are pushed apart more than the few n’s can counteract. Similarly, too many n’s compared to the p’s is bad, too. Only the right mix works.

But now there is yet another force: electric repulsion. The protons are positively charged as well, so they repel each other even more. Meanwhile, neutrons don’t care about this charge at all. That in the end means that you need often a bit more neutrons than protons for optimal stability. Especially of there are many protons.

But even if you have the right ratio of both, a nucleus with too many p’s and n’s won’t keep. Try to get a bunch of marbles in two colors, you want to arrange them in 3D in such a way that same–colored ones are as far apart as possible, while each marble touches as many different-colored ones as possible. There is no good way to do this perfectly, there will always be same-colored ones close. And the larger the number, the worse this gets for the center balls. At some size, it simply won’t hold together anymore.

Even more, if you “shake” a barely stable atom too hard, e.g. by hitting it with very intense light (_photons_) or a collision, it can become temporarily unstable. Effectively because the arrangement got disturbed away from the state where it was already barely able to stay together.

Lastly, lets quickly take a look what happens if the current arrangement is unstable:

If there are too many protons for the neutrons to counteract their repulsion, the nucleus does what we call _alpha decay_: it shoots out 2p+2n as a bundle (the nucleus of Helium-4). This usually improves the ratio, and also reduces the number of protons. In more extreme cases, especially if it was previously “shaken”, it can just explode into multiple globs; this is what happens in nuclear reactors/bombs after Uranium-235 got hit with a neutron. This is also what happens if you just stick 2 protons without a neutron together: it flies apart almost instantly.

If on the other hand there are too many neutrons, another force of nature, the _weak force_, allows a neutron to turn into a proton (plus electron and a _anti-neutrino_ both of which are shot away and don’t matter here), called _beta decay_. This again improves the ratio towards something more stable. This also happens if you only have a neutron without any proton around: after a dozen minutes or so, it turns into a proton.

Much rarer it could also happen in an almost-reverse: a proton turning into a neutron (sending away an anti-electron and a neutrino). This is rather rare, but happens in a few elements (potassium-40 for example). Commonly those elements mainly decay by one of the first two options, and only rarely by this third one. But it could even happen with the 2p stuck together, creating 1p+1n (_deuterium_); which is how the fusion in the sun works, and why it is actually extremely slow.

Its probably not an ELI5 answer, but here we go. It’s all a careful balancing act of the electromagnetic force, the weak nuclear force, and the strong nuclear force. The electromagnetic force you should be familiar with, charge and magnetism. We are really only concerned with charge here. The weak force is what’s responsible for beta decay, and the strong nuclear force is the main thing holding the nucleus together.

The electromagnetic force means that the protons in the nucleus are going to repel each other. The strong nuclear force at close distances (less than 1.7 femtometers) so the can be held together. So if a nucleus is too big, it will push itself apart with its own electrostatic repulsion. That’s why a lot of larger elements are radioactive. Alpha decay and proton ejection are both a result of this happening.

Then why aren’t super small nuclei a thing? Why don’t we have helium-2, but rather helium-4 and small amounts of helium-3? Well that’s where the weak nuclear force comes in. If we did have helium-2, it would β+ decay into deuterium (hydrogen-2). Now I’ll be honest, the weak force is the one I understand the least, but essentially it prevents the overcrowding of protons or neutrons, but basically in the helium-2, the protons are overcrowded, so it turns one into a neutron to restore balance. The same would happen in helium-6 with too many nuetrons, but would undergo beta decay instead of β+.

Plutonium-188 would likely rip itself apart in a fission reaction thanks to the electromagnetic force, but if it didn’t it would almost certainly β+ decay into something more stable.

To really mess with your brain, we cause fission of uranium-235 by adding a neutron, the resulting uranium-236 undergoes fission, but uranium-238 is not only (relatively) stable, but the most common form of uranium.

I hope this helps.

>So why wouldn’t something like Plutonium-188 be stable, since it would have 94 protons and 94 neutrons?

Firstly, There are no stable elements heavier than lead (Z=82)

This is because the strong nuclear force, has a quite short range of influence, while electrical repulsion of protons has infinite range. Therefore the larger a nucleus becomes, the less strongly one given proton is restrained against it’s mutual electrical repulsion against all other protons in the nucleus. Therefore for elements heavier than lead, you see either alpha decay (emission of a helium atom), or spontaneous fission in the case of elements heavier than uranium.

Alpha particle emission is the result of the process of quantum tunneling. It may be seen in a certain sense as a type of nuclear fission.

Secondly, The heaviest element with a stable isotope with a 1:1 ratio of z/N is element 20, calcium. Specifically the isotope calcium 40. (n being the number of neutrons and Z being the atomic number on the periodic table.)

For all heavier elements than calcium, rhe stable isotopes are always *Neutron Rich.* moreover the heavier the element is, the greater the average n/Z ratio becomes.

The only two stable proton-rich isotopes are helium-3 and hydrogen-1. H-1 being a trivial case.

This is related to the isotope Ca-20 being “doubly magic” meaning it has a magic number of both protons and neutrons. Magic numbers are analogous to the noble gasses, in the realm of electron structure. Noble gasses have completely filled electron shells causing the electrons to be in a particularly low energy state and therefore be very unreactive.

With calcium having a magic N (atomic number) it also has an unusually large number of stable isotopes (4) compared to K and Scandium. both of those have only one stable isotope. Sc-46 is just barely stable and has a strong tendency to absorb neutrons, after which it quickly decays into titanium-46 which is far more common in the earth’s crust than Scandium. In large stars, any scandium that is produced tends to be converted into titanium. So it has low abundance. This is why calcium and titanium are common in the universe at large but potassium is significantly rarer and scandium is much rarer.

Likewise isotopes that have magic numbers of either protons or neutrons are exceptionally stable because the nucleus is at a lower energy state by comparison to nearby isotopes or elements with similar neutron numbers.

Lead is another example of a magic numbered nucleus (Z=82) as such, it’s unusual in having four stable isotopes despite how heavy it is, compared to bismuth (one isotope that’s slightly unstable) and thallium (one stable and one that’s theoretically unstable but it’s decay hasn’t been observed reliably)

Therfore, it’s almost certainly impossible that Pu-188 could be formed for any length of time, however brief. There is simply not nearly enough strong interaction force to hold such a nucleus together at all without about 50 more intervening neutrons. Likewise, the isotope silver-94 (47n/47Z) itself only has a half life of about 27 milliseconds. So it decays almost instantly after being formed. Therefore you couldn’t use a particle accelerator to form Pu-188 by fusing 2 Ag-94.