Harold Bernhardt of Dunedin asks :-

Scientists are trying to make heavy atoms possessing 'magic' numbers of protons and neutrons (such as 126), which should be extra stable. What is the reason for the instability of the light atoms Technetium and Promethium, which have no stable isotopes? Are 43 and 61 'anti-magic' numbers?

Tony Signal, a theoretical particle physicist at Massey University, responded.

The discovery of the nucleus that sits at the heart of each atom is one of the greatest scientific breakthroughs. Ernest Rutherford was responsible for this discovery, which opened up the field of nuclear physics. Understanding the structure of nuclei is a complicated problem involving heavy use of quantum physics, however some of the important features can be described without too much mathematical detail.

Of all the different nuclei that can be formed out of protons and neutrons, approximately 275 are known to be stable and do not decay by radioactivity. Interestingly none of these 275 nuclei have either 43 or 61 protons, which means that the elements Technetium and Promethium are always radioactive and can only be found in tiny quantities on Earth (they can be found in uranium ores, where they are formed as products of the fission, or splitting, or uranium nuclei). The most stable isotope of Technetium (98Tc) has a half-life of 4.2 million years, while the most stable isotope of Promethium (145Pm) has a half-life of only 18 years.

While large nuclei, like those of uranium atoms, are unstable because of the electric repulsion between the many protons, the instability of Technetium and Promethium nuclei is more subtle. Within nuclei protons prefer to pair-off with each other, and the same goes for neutrons. We see a similar pairing effect in chemical bonding, with pairs of electrons giving a stable covalent bond that lowers the energy of the compound. Some 60 per cent of all stable nuclei have even numbers of both protons and neutrons (‘even-even’ nuclei), whereas only 5 stable nuclei have odd numbers of both protons and neutrons (‘odd-odd’ nuclei). We also know that most nuclei have the protons and neutrons packed close together with nearly constant density, similar to a droplet of liquid made up of roughly evenly spaced molecules. Quantum mechanical considerations predicts that certain numbers of protons or neutrons will be very stable; these so-called magic numbers are 2, 8, 20, 28, 50, 82 and 126.

Some nuclei, such as 16O8 and 208Pb82, have both proton and neutron numbers being magic numbers, and are known as ‘doubly-magic’. Present-day experiments are investigating whether there are any nuclei with 126 protons.

In the case of Technetium, the shell model predicts that isotopes of either Molybdenum (Z = 42) or Ruthenium (Z = 44) will be more stable than those of Technetium with the same mass number. The unpaired proton in the Technetium nucleus is energetic, so it is favourable either for that proton to turn into a neutron (by capturing an electron) or for one of the neutrons in the nucleus to turn into a proton (via beta decay), and join up with the previously unpaired proton. Similar considerations also hold for Promethium, where the nearby isotopes of Neodymium or Samarium are more energetically favoured.

The Technetium isotope 99Tc is used as a radioactive tracer in medical applications, where it has an easily detectable gamma ray emission, and a useful half-life of around 6 hours. This is a low risk procedure because Technetium has no biological function and is not absorbed by body tissues.