Why is technetium unstable?

Question

Is there a simple account of why technetium is unstable?

From the Isotopes section of Wikipedia's article on Technetium:

Technetium, with atomic number (denoted Z) 43, is the lowest-numbered element in the periodic table that is exclusively radioactive. The second-lightest, exclusively radioactive element, promethium, has an atomic number of 61. Atomic nuclei with an odd number of protons are less stable than those with even numbers, even when the total number of nucleons (protons + neutrons) are even. Odd numbered elements therefore have fewer stable isotopes.

It would seem that simply its atomic number is part of the reason why it is unstable, though this just pushes back the mystery back one step for me: why are nuclei with even atomic number more stable? And why then are all of the elements from 45 through 59 stable — notably including silver (Z=47) and iodine (Z=53) — not to mention higher odd-proton nuclei such as gold (Z=79)?

Even the most stable isotope of technetium has a half-life less than a hundredth that of uranium-235, which has a half life of 703.8Ma:

The most stable radioactive isotopes are technetium-98 with a half-life of 4.2 million years (Ma), technetium-97 (half-life: 2.6 Ma) and technetium-99 (half-life: 211,000 years) [...] Technetium-99 (99Tc) is a major product of the fission of uranium-235 (235U), making it the most common and most readily available isotope of technetium.

It's perhaps an unfair comparison, as uranium has an even atomic number (however that is suppose to help mitigate its instability); but it also has nearly twice the number of protons. This deepens the mystery for me. Even granted that Tc has no stable isotopes, how does it come to be so unstable that all of its isotopes are essentially absent naturally, compared for instance to uranium-235?

(This question is a specific case of an earlier question on synthetic isotopes.)

Answer 1

This is really a comment, since I don't think there is an answer to your question, but it got a bit long to put in as a comment.

If you Google for "Why is technetium unstable" you'll find the question has been asked many times in different forums, but I've never seen a satisfactory answer. The problem is that nuclear structure is much more complex than electronic structure and there are few simple rules.

Actually the question isn't really "why is technetium unstable", but rather "why is technetium less stable than molybdenum and ruthenium", those being the major decay products. Presumably given enough computer time you could calculate the energies of these three nuclei, though whether that would really answer the "why" question is debatable.

Response to comment:

The two common (relatively) simple models of the nucleus are the liquid drop and the shell models. There is a reasonably basic description of the shell model here, and of the liquid drop model here (there's no special significance to this site other than after much Googling it seemed to give the best descriptions).

However if you look at the sction of this web site on beta decay, at the end of paragraph 14.19.2 you'll find the statement:

Because the theoretical stable line slopes towards the right in figure 14.49, only one of the two odd-even isotopes next to technetium-98 should be unstable, and the same for the ones next to promethium-146. However, the energy liberated in the decay of these odd-even nuclei is only a few hundred keV in each case, far below the level for which the von Weizsäcker formula is anywhere meaningful. For technetium and promethium, neither neighboring isotope is stable. This is a quali­tative failure of the von Weizsäcker model. But it is rare; it happens only for these two out of the lowest 82 elements.

So these models fail to explain why no isotopes of Tc are stable, even though they generally work pretty well. This just shows how hard the problem is.