What specific nuclear and electronic properties make these two elements (Tc & Pm) almost disappear from solar and galactic abundance tables?
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All isotopes of the elements technetium (Tc) and promethium (Pm) are radioactive. Their isotopes with the longest half-life are:
- $\rm ^{97}_{43}Tc$ ($4.21 \cdot 10^6$ years), $\rm ^{98}_{43}Tc$ ($4.2 \cdot 10^6$ years)
- $\rm ^{145}_{61}Pm$ ($17.7$ years)
Therefore any technetium and promethium produced in supernova eruptions decays quickly.
This immediately raises the deeper question, why these relatively low-mass elements don't have any stable isotopes. This is asked in Why is technetium unstable? The accepted answer there covers technetium and promethium.

Thomas Fritsch
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Perhaps you could briefly mention why such relatively low mass elements have no stable isotopes. – PM 2Ring Jun 27 '19 at 18:29
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PM That is probably what I should have asked. Some authors say (Scerri) that Tc may have been discovered long before it was synthesized but the astro people say that neither exists. Anyway, thanks for the clarification. – Harry Jun 27 '19 at 18:44
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1@PM2Ring There is another deeper question asking Why is technetium unstable?. Its accepted answer covers technetium and promethium. – Thomas Fritsch Jun 27 '19 at 19:04
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Looks good, Thomas. @Harry Do the answers at the question Thomas just linked satisfy you? – PM 2Ring Jun 27 '19 at 19:16
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Yes. Thanks to you and Thomas I have a head start on solving a big mystery. – Harry Jun 27 '19 at 19:33