Re: Why does the element Tc not exist in nature?

Heidi:

I like the way you phrased your question.  It does appear that there is 
something "special" about the element technetium because none of the 
isotopes of technetium are stable.

There are no stable isotopes of any element above bismuth, but for 
elements of atomic number less than bismuth, only technetium and 
promethium have no stable isotopes.

When I am asked the question of why they are not stable, I usually begin 
by expressing surprise that ANY element above hydrogen is stable.  That 
usually results in either a frown or a blank look from my questioner.  
Then I explain that if you believe that the laws of electrostatics still 
hold in the nucleus of atoms, there must be tremendous forces of repulsion 
pushing the protons apart from each other when they (with their "like" 
charges) get so very close to each other.  It is possible to calculate 
these forces, and they increase dramatically as more and more "like" 
charges are added to the small volume of the nucleus.  I try to avoid 
getting too mathematical, at least initially.

Why, then, are most isotopes of most elements stable for the lower atomic 
numbers?  The reason is that there must be a much stronger force at work 
in the nucleus and it must be a force that falls off in magnitude quickly 
with distance or else we would see some effects of this force on the 
orbital electrons of the atoms (and we do not).  So, this very strong, 
short-range force - called the nuclear force - overpowers the natural 
electrostatic repulsion of all those positive charges in the nucleus.  At 
least it does so for a while.  Eventually, as protons are added, you will 
reach a point (bismuth) above which nothing is completely stable.

The actual calculation of forces in the nucleus is very difficult for more 
complex atoms and involves the nuclear quantum numbers of the particles in 
place there.  For technetium and promethium (as well as all the heavier 
elements above bismuth) the cohesive forces "caused" by the particular 
combinations of quantum numbers is just not as strong as the repulsive 
forces of the protons jammed together in such a small volume.  As a 
result, all isotopes of those elements are radioactive (ie, unstable).

So, to answer your question in similar terms, what is so "special" about 
technetium lies in the quantum numbers of the protons and neutrons that 
make up its nucleus, and the fact that the cohesive short-range forces 
generated by these particles is not sufficient to overcome the strong 
repulsive forces caused by the 43 protons in close proximity to each other.