Eric Scerri has raised an interesting question about why technetium, a
relatively light element, has no stable isotopes. I still claim the
question is not really the correct question.
The size of the nucleus is indeed a determining factor for alpha decay. The
size of the nucleas is indeed a determining factor for spontaneous fission.
However, for beta decay, which is the decay mode for the technetium
isotopes, the size of the nucleus has nothing to do with stability. The
determining factor for beta decay is the proton/neutron ratio.
As we examine nuclides near the line of beta stability, the even-even
nuclides will have an advantage due to fully paired protons and neutrons.
The even-odd (protons-neutrons) is next best, the odd-even are less good
than that, and the odd-odd are the worst.
Next, we must not look within the isotopes of Tc; rather we must look at the
isobars in the region where Tc might have a stable isotope. On a Segre
Chart, we see that the line of beta stability runs through the Z=43 region
at about N = 55. That means the stable nuclides in that region have A of
about 98. So we need to study a range of perhaps 94 < A < 102 to see which
Z will "win" for each isobar in this region.
For A = 94, Mo (even-even) wins.
For A = 95, Mo (even-odd) wins again.
For A = 96, Mo and Ru (both even-even) win over Tc (odd-odd)
For A = 97, Mo (even-odd) wins by a small margin of 0.320 MeV over 97Tc
(odd-even). This would have been one of Tc's best chances for a stable
isotope.
For A = 98, Mo and Ru (even-even) both win over Tc (odd-odd)
For A = 99, Ru (even-odd) wins over Tc (odd-even) by a margin of 0.294 Mev.
This would have been Tc's best chance for a stable isotope.
For A = 100, Mo and Ru (even-even) both win over Tc (odd-odd).
... and so forth.
Please note, in an earlier post for which I was using 1970 data, I stated
that 97Tc was closest to being stable. That older source had an estimated Q
value for 99Tc that was higher than the more current number in the 2002
chart. Therefore I need to update my statememt about which Tc isotopes are
closest to stability. 99Tc is closest by a slim margin, then 97Tc ( a
slight loser), then 98Tc (an odd-odd fairly big loser).
In his original post, Eric state that surely this is not just an even/odd
thing. Actually it surely is, because once you get rreal close to the beta
stability, the even/odd difference can make the final difference. This
happens throughout beta decay. There is nothing special about Tc other than
the fact that it loses out on being the most stable isobar for every isobar
in the region where Tc might have been stable.
BTW, perhaps an equally valid question (more valid?) would be to ask why we
don't have more odd-Z nuclides that do not have any stable isotope. I
suggest it's just the luck of the draw in terms of where the neutron and
proton closed shells fall, and then add pairing to that.
I still maintain that people wanting to know more about nuclear stability
need to study beta decay, and do so in terms of isobars, which is where
beta-decay occurs. The class-handout I wrote about beta-decay can be found
at...
Because technetium is such an interesting case, I will append some more info
to that handout, including the isobar mass(energy) parabolas for A values in
thie vicinity of the Segre Chart. When I have added those figures, I will
let you know. It might take a couple days.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
1 University Drive
Bluffton, OH 45817
419.358.3270
edmiston@bluffton.edu