11.1 Nuclear structure and stability  (Page 4/17)

The nuclei that are to the left or to the right of the band of stability are unstable and exhibit radioactivity    . They change spontaneously (decay) into other nuclei that are either in, or closer to, the band of stability. These nuclear decay reactions convert one unstable isotope (or radioisotope    ) into another, more stable, isotope. We will discuss the nature and products of this radioactive decay in subsequent sections of this chapter.

Several observations may be made regarding the relationship between the stability of a nucleus and its structure. Nuclei with even numbers of protons, neutrons, or both are more likely to be stable (see [link] ). Nuclei with certain numbers of nucleons, known as magic numbers , are stable against nuclear decay. These numbers of protons or neutrons (2, 8, 20, 28, 50, 82, and 126) make complete shells in the nucleus. These are similar in concept to the stable electron shells observed for the noble gases. Nuclei that have magic numbers of both protons and neutrons, such as ${}_2^4\text{He},$ ${}_8^{16}\text{O},$ ${}_{20}^{40}\text{Ca},$ and ${}_{82}^{208}\text{Pb},$ are called “double magic” and are particularly stable. These trends in nuclear stability may be rationalized by considering a quantum mechanical model of nuclear energy states analogous to that used to describe electronic states earlier in this textbook. The details of this model are beyond the scope of this chapter.

The relative stability of a nucleus is correlated with its binding energy per nucleon    , the total binding energy for the nucleus divided by the number or nucleons in the nucleus. For instance, we saw in [link] that the binding energy for a ${}_2^4\text{He}$ nucleus is 28.4 MeV. The binding energy per nucleon for a ${}_2^4\text{He}$ nucleus is therefore:

In [link] , we learn how to calculate the binding energy per nucleon of a nuclide on the curve shown in [link] .

Key concepts and summary

An atomic nucleus consists of protons and neutrons, collectively called nucleons. Although protons repel each other, the nucleus is held tightly together by a short-range, but very strong, force called the strong nuclear force. A nucleus has less mass than the total mass of its constituent nucleons. This “missing” mass is the mass defect, which has been converted into the binding energy that holds the nucleus together according to Einstein’s mass-energy equivalence equation, E = mc ² . Of the many nuclides that exist, only a small number are stable. Nuclides with even numbers of protons or neutrons, or those with magic numbers of nucleons, are especially likely to be stable. These stable nuclides occupy a narrow band of stability on a graph of number of protons versus number of neutrons. The binding energy per nucleon is largest for the elements with mass numbers near 56; these are the most stable nuclei.

Key equations

• E = mc ²

Chemistry end of chapter exercises