Page 52 - Radiochemistry and nuclear chemistry

CHAPTER 3

Nuclear Mass and Stability

Contents

3.1. Patterns of nuclear stability 41
3.2. Neutron to proton ratio 43
3.3. Mass defect 45
3.4. Binding energy 47
3.5. Nuclear radius 48
3.6. Semiempirical mass equation 50
3.7. Valley of/3-stability 51
3.8. The missing elements: 43Tc and ePm 53
3.8.1. Promethium 53
3.8.2. Technetium 54
3.9. Other modes of instability 56
3.10. Exercises 56
3.11. Literature 57

3. I. Patterns of nuclear stability

There are approximately 275 different nuclei which have shown no evidence of radioactive
decay and, hence, are said to be stable with respect to radioactive decay. When these nuclei
are compared for their constituent nucleons, we find that approximately 60 % of them have
both an even number of protons and an even number of neutrons (even-even nuclei). The
remaining 40% are about equally divided between those that have an even number of
protons and an odd number of neutrons (even-odd nuclei) and those with an odd number
of protons and an even number of neutrons (odd-even nuclei). There are only 5 stable nuclei
known which have both an odd number of protons and odd number of neutrons (odd-odd
50
nuclei); 2H, 6Li, I~ I~N, and 23 V. It is significant that the first stable odd-odd nuclei are
abundant in the very light elements (the low abundance of 12H has a special explanation, see
Ch. 17). The last nuclide is found in low isotopic abundance (0.25 %) and we cannot be
certain that this nuclide is not unstable to radioactive decay with extremely long half-life.
Considering this pattern for the stable nuclei, we can conclude that nuclear stability is
favored by even numbers of protons and neutrons. The validity of this statement can be
confirmed further by considering for any particular element the number and types of stable
isotopes; see Figure 3.1. Elements of even atomic number (i.e. even number of protons)
are characterized by having a relatively sizable number of stable isotopes, usually 3 or
more. For example, the element tin, atomic number 50, has 10 stable isotopes while

41