Technetium & Promethium, a Question

Quadlok · Post by **Quadlok** » 2005-05-13 08:05pm

Why are these elements radioactive and not found in nature? At #s 43 and 61 on the periodic table, they shouldn't be heavy enough to have an unstable nucleus, the next highest radioactive element is Actinium at 89 and the next highest man made element is Neptunium at 93. So whats the deal?

Kuroneko · Post by **Kuroneko** » 2005-05-13 08:58pm

Nucleons are half-spin particles, so they can occupy the same state by having opposite spin (cf. Pauli exclusion principle). This is a problem nuclei of odd atomic numbers because the protons cannot pair up with each other in this fashion. Actually, the same goes for the number of neutrons, but beyond this even/odd stability rule, Tc and Pm are simply unlucky.

Quadlok · Post by **Quadlok** » 2005-05-13 09:09pm

Kuroneko wrote:Nucleons are half-spin particles, so they can occupy the same state by having opposite spin (cf. Pauli exclusion principle). This is a problem nuclei of odd atomic numbers because the protons cannot pair up with each other in this fashion. Actually, the same goes for the number of neutrons, but beyond this even/odd stability rule, Tc and Pm are simply unlucky.

So there's no real reason beyond random chance? Besides the pairing problem, that is.

And how the hell did you get so smart, anyway? Every time someone asks a question about science, bam, there's Kuroneko giving a concise accurate answer. Its spooky.

Kuroneko · Post by **Kuroneko** » 2005-05-13 09:36pm

The pairing rule is important; evenness is favored by stable nuclei to a significant degree. One would be hard-pressed to find a stable atom with an odd number of protons and and odd number of neutrons, for example (although IIRC there are some). I think you overestimate my knowledge, however. My area is actually mathematics (which is why I like general relativity, being basically a giant exercise in differential geometry), and although I have some familiarity with basic physics and some quantum mechanics, it's not very deep.

Quadlok · Post by **Quadlok** » 2005-05-13 09:47pm

Kuroneko wrote:The pairing rule is important; evenness is favored by stable nuclei to a significant degree. One would be hard-pressed to find a stable atom with an odd number of protons and and odd number of neutrons, for example (although IIRC there are some). I think you overestimate my knowledge, however. My area is actually mathematics (which is why I like general relativity, being basically a giant exercise in differential geometry), and although I have some familiarity with basic physics and some quantum mechanics, it's not very deep.

Well, maybe you're just really good at playing to your strengths. But why is it that of the first 88 elements, a good number of which assumedly have an odd number of nuetrons and protons, that it is only these two that are unstable enough to not be present in nature? It just doesn't seem right.

Kuroneko · Post by **Kuroneko** » 2005-05-13 11:00pm

Quadlok wrote:But why is it that of the first 88 elements, a good number of which assumedly have an odd number of nuetrons and protons, that it is only these two that are unstable enough to not be present in nature? It just doesn't seem right.

If you inspect this table, the disparity between even-proton nuclei and odd-proton ones is rather striking. I don't have the exact statistics, but based on that table, I estimate that only about 1/5 of all stable nuclei have an odd number of protons, and I still can't find a single odd-odd proton-neutron configuration (then again, I haven't actually looked very hard). For odd atomic numbers, having more than one stable isotope is very rare (see for yourself on that table), directly because of the lack of pairing. Put that way, it's not all that difficult to accept that some of them would have none at all. Multiple stable isotopes is almost exclusively in the domain of even-proton nuclei.

tharkûn · Post by **tharkûn** » 2005-05-14 02:34am

Well, maybe you're just really good at playing to your strengths. But why is it that of the first 88 elements, a good number of which assumedly have an odd number of nuetrons and protons, that it is only these two that are unstable enough to not be present in nature? It just doesn't seem right.

Nuclear packing is done following some quantum rules similar to electronic packing. While one can do a decent job approximating the strength of the Strong force simply by counting up protons and neutrons, in reality you need to look at a more advanced model. In that model we find that for these two odd Z you can't assign quantum numbers in a manner that makes allows the cohesive forces to overpower the repulsive electromagnetic force.

This is the same phenomena by which you can have different decay pathways for the "same" isotope - the particles are just packed in a different manner. Nuclear packing is more complex than electronic packing so it is not surprising that two oddities arise.

In any event these nuclei are the result of spontaneous nuclear fission of U-238 and trace Tc (< ng/kg) quantities have been recovered from natural pitchblende; both show up in stellar matter with very good instruments.

Veramocor · Post by **Veramocor** » 2005-05-14 07:36pm

Kuroneko wrote:
Quadlok wrote:But why is it that of the first 88 elements, a good number of which assumedly have an odd number of nuetrons and protons, that it is only these two that are unstable enough to not be present in nature? It just doesn't seem right.
If you inspect this table, the disparity between even-proton nuclei and odd-proton ones is rather striking. I don't have the exact statistics, but based on that table, I estimate that only about 1/5 of all stable nuclei have an odd number of protons, and I still can't find a single odd-odd proton-neutron configuration (then again, I haven't actually looked very hard). For odd atomic numbers, having more than one stable isotope is very rare (see for yourself on that table), directly because of the lack of pairing. Put that way, it's not all that difficult to accept that some of them would have none at all. Multiple stable isotopes is almost exclusively in the domain of even-proton nuclei.

Well the first one is pretty easy to find:

Odd-Odd: Deuterium: Stable
Odd-Even: Ttritium: Unstable

Kuroneko · Post by **Kuroneko** » 2005-05-14 07:43pm

Aa! Rather obvious, in hindsight. :oops:
Wonder how many stable odd/odd configurations there are total.

tharkûn · Post by **tharkûn** » 2005-05-14 11:35pm

Well the first one is pretty easy to find:

Hydrogen is the bastard element. In nuclear physics you it should be regarded as the exception until it is proven to meet the rule. Think about it for a second, in hydrogen you have exactly one proton so there is no other proton to create a repulsive force, at least to a first order approximation.

Much like its electronic structure, the nuclear structure of hydrogen is ridiciously simple compared to the many body problems of more complex elements.