Why Can't Technetium Keep It Together?

Technetium is a radioactive element. VERY radioactive. Tc-99, the most common isotope, has a half life of just six hours; it is vanishingly hard to find in nature. The artificial Tc-97 lasts million of years but it’s way rarer and is, well, artificial.

I don’t get this. Technetium is element 43 on the periodic table. Why is THIS element unable to hold itself together when all the elements around it are stable? It is bordered by molybdenum (42) and ruthenium (44) both stable, and if you’re wondering if it’s an odd/even number thing niobium (41) and rhodium (45) have stable forms, too. Is it its place in the periods? Above it is manganese, which is stable, and below it is rhenium. Both have stable isotopes.

So I don’t get it.

I’m no physicist, but i think it has more to do with the number of neutrons. Or the protob/neutron ratio.

It certainly doesn’t have anything to do with the periods on the periodic table. Those involve how the electrons interact, and have nothing to do with the nucleus beyond the nucleus’ total charge.

The fact that it’s an odd number is relevant, because overall, having an even number of protons (and of neutrons) is typically more stable than having an odd number: Roughly speaking, if there’s “room” for one proton in a nucleus, then there’s also “room” for another, with the opposite spin. But of course, that’s not the whole picture, because as you note, elements two (or four or six…) above or below it are stable.

Ultimately, it’s a matter of the quantum mechanical waveforms of all of the individual protons and neutrons, and how they interact, just like the chemical properties of elements are a matter of the waveforms of the electrons. But it’s more complicated for two reasons: First, the waveform of each particle depends on those of all of the other particles. This is also true of the electrons, but with the electrons, you can get away with calculating what each one would be by itself, and then tweaking each of those calculations based on the effect of the others, and iterating a few times if necessary (usually, just the first order perturbations are enough). But for the protons and neutrons, the influence of the others is much stronger, such that what one would do in isolation is no guide at all to what it would do surrounded by others. And second, the interactions between the electrons are all via the electromagnetic force, which we understand very well, but the interactions between protons are mostly via the strong force, which we understand only very poorly.

[Barbie voice] Chromodynamcis is hard. [/Bv]

Technetium-99 has a half life of 21,000 years. What has a half life of 6 hours is an isomer of T-99, designed 99m-Tc. Since isomers often last less than a billionth of a second, 6 hours is a really long-lived isomer.

Missing an order of magnitude there? I think that it’s 211,000 years.

But, it is still an interesting element in that it’s the lightest that is has no stable isotope. Also interesting is that most of its isotopes have metastable states that are much longer than those found in most other elements. Many of its metastable states actually have longer half lives than the ground state.

Best I can tell as to why has to do with the nuclear shell model and how it just sticks out a bit due to the arrangement involved in 43 protons, giving it a bit of a higher binding energy than those around it. That means that the ground state is closer in energy to the metastable states, and also means that the ground state has a higher energy than elements around it, giving it an “incentive” to decay.

I’m not sure that anyone really has a definitive answer, at least not that I’ve seen, as to why it works out this way.

Oops. Thanks.

In a sense, it’s partially due to “bad luck”. Elements have to share stability with their neighbors. In particular, taking two adjacent elements, and considering two different isotopes with the same number of nucleons (called isobars), at most one of them can be stable.

Consider 96Mo vs. 96Tc. 96Tc has 43 protons and 53 neutrons, while 96Mo has 42 protons and 54 neutrons. As it happens, 96Tc undergoes electron capture, converting one of the protons into a neutron, which turns it into 96Mo. On the other hand, we have 98Tc, which undergoes beta decay, converting a neutron into a proton, turning it into 98Ru.

Essentially we’re just assuming that if beta decay or electron capture can happen, it will happen. The isotope with the higher energy state will inevitably decay into the other. The reverse won’t happen due to conservation of energy, so it’ll either be stable then or decay into some third element.

Most elements, even if the nucleus isn’t a particularly stable one, will at least get lucky with one or two isotopes. For instance, going two down to Niobium, it has only a single stable isotope 93Nb. So even though it has an odd number of protons, and that’s not great for stability, it still managed to hold onto one (note that this implies 93Mo is unstable–which it is).

So it’s not hard to imagine that out of nearly a hundred natural elements, there would be a couple that lose every battle with both of their neighbors on the stability front. Of course there are good technical reasons why one isobar would be more stable than another, but the details are so involved that it ends up looking a lot like a coin flip in some cases.

But then, helium-3 (two protons and one neutron with two electrons) is stable.

Tritium, however, is not stable: it emits an electron and turns to 3He. 3Li is also nowhere close to stable (really too unstable to be measured; the 3 protons just fly apart immediately).

Having too many protons is a problem. But as I mentioned above, so is having a neighbor with the same number of nucleons but in a lower energy state.

Isn’t the same true for He-2? My understanding is that it’s impossible to have anything meaningfully called a nucleus with more than one nucleon unless at least one is a neutron, just from how the strong force works. You need there to be a neutron to be exchanging virtual particles with a proton to (in some sense that I don’t totally understand) create the force needed to keep the nucleus together. If there’s just protons, that exchange can’t happen. You can force two protons as close as you want together, but they’ll never display the behavior associated with a nucleus. Other very unstable particles will at least pretend for a small fraction of a second that nothing’s wrong.

Yes; the point I was making was just about isobars: here, all nuclei with exactly three nucleons. There are four possibilities: 0p3n, 1p2n, 2p1n, and 3p0n.

0 protons/3 neutrons isn’t even an atom. And 3p0n flies apart immediately since the Coulomb force overcomes the (residual) strong force. But 1p2n and 2p1n are plausible, and correspond to tritium and 3He. One of them is going to have a lower energy level than the other, and the other is going to decay (via beta decay or electron capture) into the more stable one. As it happens, 3He wins that battle in this case.

The strong force still pulls protons together. It’s just that the Coulomb force exceeds it. So if all you have is protons, it’ll just fly apart. But if you “dilute” the Coulomb force with neutrons, then eventually the strong force becomes more powerful (since it is pretty much the same between neutrons and protons).

Yes and no. An attempt at a “nucleus” with all of one type of nucleon and none of the other (two or more neutrons and no protons, or two or more protons and no neutrons) will immediately fly apart, but because of the strong force, not the Coulomb force. For nuclei that small, the Coulomb force is insignificant compared to the strong force (it’s only for larger nuclei, where some of the nucleons are significantly further apart, that the Coulomb force becomes relevant). And the strong force can be either attractive or repulsive, depending on circumstances that are difficult to explain without a lot more grounding in quantum mechanics, but suffice to say that any situation with all of the nucleons being the same species is always one of the repulsive situations.

I hadn’t really thought of the strong force as being repulsive before, but that seems to make sense, otherwise, you’d have clumps of neutrons that stuck together. It’d be unstable, but unstable on the order of neutron decay, so would tend to hold together for a few minutes or so.

Now I’m wondering to what extent a deuterium nucleus is a proton and a neutron, and to what extent it’s just six quarks zooming around, trading places with each other.

Aren’t we all just quarks zooming around, trading places with each other?

Keep your gluons away from me!

Maybe the real treasure is the gluons we interacted with along the mean free path?

It’s even worse than that. It’s best understood some number of wavefunctions oscillating in quantum fields interacting with each other in a way that causes us to be able to more easily understand it as 6 particles that are grouped into 2 different kinds of nucleons. The entirety of existence is just currently best understood as wavefunctions oscillating in quantum fields. One day perhaps we will understand reality even better than this, just as today we understand it better than just quarks, gluons, and leptons, which was better than just neutron, protons and electrons, which was better than just various types atoms.

It’s oscillating quantum fields all the way down.