Page 64 - Radiochemistry and nuclear chemistry

Nuclear Mass and Stability 53

to the fight of Figure 3.1 and looking down the valley. The isobars located on the sides of
the parabola (or slope of the valley) are unstable to radioactive decay to more stable
nuclides lower on the parabola, though usually the most stable nucleus is not located exactly
at the minimum of the parabola. Nuclides on the left hand side of the parabola (lower
atomic numbers) are unstable to decay by B-emission. Isobars to the fight of the valley of
stability are unstable to/3 + decay or electron capture. At the bottom of the valley the
isobars are stable against B- decay. The curved line in Figure 3.1 is calculated for
maximum stability according to (3.8), and indicates the theoretical bottom of the valley.
The minimum of the curve can be calculated from (3.8) to be
Z = 2A/[4 + (ac/aa)A 2/3] (3.10)

and is shown in Figure 3.1. For small A values (3.10) reduces to Z = A/2 or N = Z; thus
the bottom of the stability valley follows the N = Z line as indicated in Figure 3.1 for the
lighter nuclides.
A closer analysis of (3.9) makes us expect that the last term gives rise to three different
isobaric parabola depending on whether the nuclei are odd-A (even-odd or odd-even),
odd-odd, or even-even (Fig. 3.6). In the first case, in which the mass number is odd, we
find a single parabola (I); whether all beta decay leads to changes from odd-even to
even-odd, etc. For even mass numbers one finds a double parabola (II) - (V). When the
individual nuclear properties are considered, the difference between the curves for the
odd-odd and even-even nuclei may lead to alternatives with regard to the numbers of
possible stable isobars: it is possible to find three stable isobars (case V) although two (case
IV) are more common. Although the odd-odd curve always must lie above the even-even
curve, still an odd-odd nucleus may become stable, as is shown for case II.

3.8. The miming elements: 43Tc and 61Pm

Among the stable elements between iH and 82Pb two elements are "missing': atomic
number 43, named technetium (Tc), and atomic number 61, promethium (Pin). Though
these elements can be produced through nuclear reactions and also have been found to exist
in certain stars, they are not found on earth because their longest lived isotopes have much
too short half-lives for them to have survived since the formation of our planet. This can
be understood by considering the valley of B-stability. For pedagogic reasons we will first
discuss promethium.

3.8.1. Promethium

The valley of 0-stability for Z = 61 shows a minimum around mass number A = 146,
for which the isotopes are either of the even-even or of the odd-odd type. Thus the binding
energy curve should exhibit two isobar parabolas, as illustrated in Figure 3.7; the decay
energy Q is released bind'm.g energy. 146pm has a 5.5 y half-life and decays either by
electron capture (63%) to 140 Nd or by B--emission (37%) to 146 Sm, who both are more
stable (i.e. have a larger nucleon binding energy); the nuclear binding energy is given on