Technetium and
promethium are unusual light elements in that they have no stable isotopes. Using the
liquid drop model for atomic nuclei, one can derive a semiempirical formula for the binding energy of a nucleus. This formula predicts a "
valley of beta stability" along which
nuclides do not undergo beta decay. Nuclides that lie "up the walls" of the valley tend to beta decay towards the center (by emitting an electron, emitting a
positron, or capturing an electron). For a fixed number of nucleons
A, the binding energies lie on one or more
parabolas, with the most stable nuclide at the bottom. One can have more than one parabola because isotopes with an even number of protons and an even number of neutrons are more stable than isotopes with an odd number of neutrons and an odd number of protons. A single beta decay then transforms one into the other. When there is only one parabola, there can be only one stable isotope lying on that parabola. When there are two parabolas, that is, when the number of nucleons is even, it can happen (rarely) that there is a stable nucleus with an odd number of neutrons and an odd number of protons (although this happens only in five instances:
2H,
6Li,
10B,
14N and
180mTa). However, if this happens, there can be no stable isotope with an even number of neutrons and an even number of protons (180 is an exception, and 180mTa is only
observationally stable). For technetium (
Z = 43), the valley of beta stability is centered at around 98 nucleons. However, for every number of nucleons from 94 to 102, there is already at least one stable nuclide of either
molybdenum (
Z = 42) or
ruthenium (
Z = 44), and the
Mattauch isobar rule states that two adjacent
isobars cannot both be stable. == See also ==