Band of stability

The ratios of stable isotopes (red dots) fall within a narrow range, referred to as the "belt of stability." For light isotopes of small atomic number the stable ratio is 1 1. For heavier isotopes the ratio gradually increases to about 1.5 1. Isotopes outside the band of stability are unstable and radioactive. There are no stable isotopes for elements of atomic number greater than 83 (Bi). 

Figure 17.13 is a plot of mass number against atomic number for known nuclides. Stable nuclei are found in a band of stability surrounded by a sea of instability, the region of unstable nuclides that decay with the emission of radiation. For atomic numbers up to about 20, the stable nuclides have approximately equal numbers of neutrons and protons, and so A is close to 2Z. For higher atomic numbers, all known nuclides—both stable and unstable—have more neutrons than protons, and so A > 2Z. 

We can use Fig. 17.13 to predict the type of disintegration that a radioactive nuclide is likely to undergo. Nuclei that lie above the band of stability are neutron rich they have a high proportion of neutrons. These nuclei tend to decay in such a way that the final n/p ratio is closer to that found in the band of stability. For example, a l4C nucleus can reach a more stable state by ejecting a (3 particle, which reduces the n/p ratio as a result of the conversion of a neutron into a proton (Fig. 17.15) ... 

Nuclides that lie below the band of stability have a low proportion of neutrons and are classified as proton rich. These isotopes tend to decay in such a way that the... 

FIGURE 17.15 Three different ways of reaching the band of stability- (black). Nuclei that are neutron rich (blue region) tend to convert neutrons into protons by P emission nuclei that are proton rich (red) tend to reach stability (black) by emitting a positron, capturing an electron, or emitting a proton. 

Use the band of stability to predict the types of decay that a given radioactive nucleus is likely to undergo (Self-Test 17.3). 

The following nuclides lie outside the band of stability. Predict whether each is most likely to undergo p decay, P"1 decay, or a decay, and identify the daughter nucleus ... 

Actinium-225 decays by successive emission of three u particles, (a) Write the nuclear equations for the three decay processes, (b) Compare the neutron-to-proton ratio of the final daughter product with that of actinium-225. Which is closer to the band of stability ... 

Example H,0+(aq) + HS"(s) - H2S(g) + H20(1). proton emission A nuclear decay process in which a proton is emitted. In proton emission, the mass and charge numbers of the nucleus both decrease by 1. proton-rich nucleus A nucleus that has a low proportion of neutrons and lies below the band of stability. proton transfer equilibrium The equilibrium involving the transfer of a hydrogen ion between an acid and a base. 

Although all three of these isotopes of silicon are radioactive, the heaviest of them, 34Si, lies farthest from the band of stability and it has the shortest half-life. Generally, the farther a nuclide lies from the band of stability, the shorter its half-life. There are numerous exceptions to this general rule and we will discuss some of them here. First, consider these cases ... 

Although 28Mg is farther from the band of stability than is 27Mg, the former is an even-even nuclide while the latter is an even-odd nuclide. As we have seen earlier, even-even nuclides tend to be more stable. Consequently, the even-even effects here outweigh the fact that 28Mg is farther from the band of stability. Another interesting case is shown by considering these isotopes of chlorine ... 

In this case, the 38i7Cl is an odd-odd nucleus, whereas 3917C1 is an odd-even nucleus. Thus, even though 3917C1 is farther away from the band of stability, it has a slightly longer half-life. Finally, let us consider two cases where both of the nuclei are similar in terms of numbers of nucleons. Such cases are the following ... 

In this case, there is no real difference with respect to the even/odd character. The large difference in half-life is related to the fact that 39i7C1 is farther from the band of stability than is 39i8Ar. This is in accord with the general principle stated earlier. While specific cases might not follow the general trend, it is generally true that the farther a nuclide is from the band of stability, the shorter its half life will be. 

FIGURE 17.13 The manner in which nuclear stability depends on the atomic number and the mass number. Nuclides along the narrow black band (the band of stability) are generally stable. Nuclides in the blue region are likely to emit a (3 particle, and those in the red region are likely to emit an a particle. Nuclei in the pink region are likely to emit either positrons or to undergo electron capture. 

Nuclides that lie below the band of stability have a low proportion of... 

The following nuclides lie outside the band of stability. Predict whether they are most likely to... 

The ratio of neutrons to protons gradually increases for elements heavier than calcium, giving a curved appearance to the band of stability. The most abundant stable isotope of bismuth, for example, has 126 neutrons and 83 protons (TsBi). 

Q Atoms whose nuclei are above the band of stability (high neutron-to-proton ratio) can lower their numbers of neutrons by undergoing beta emissions. The typical pattern for these is that the mass number (number of neutrons + number of protons) is greater than the atomic weight. Remember that beta emissions convert neutrons into protons and beta particles. 

The dots representing 256 known stable nuclei cluster over a range of neutron-proton ratios, which are referred to as a band of stability. This band of stability is shown in yellow in Figure 6. 

The ratio of neutrons to protons defines a band of stability that includes the stable nuclei. 

Calculate the neutron-proton ratios for the following nuclides, and determine where they lie in relation to the band of stability. 

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