Question 19.3: Predicting the Type of Radioactive Decay Predict whether eac...

(a) Magnesium-28 has 16 neutrons and 12 protons, so N/Z = 1.33. However, for Z = 12, you can see in Figure 19.4 that stable nuclei should have an N/Z ratio of about 1. Alternatively, on the periodic table you can look up the atomic mass of magnesium, which is 24.31 amu; a magnesium nuclide with a mass number of 28 is too heavy to be stable because the N/Z ratio is too high. Therefore, Mg-28 undergoes beta decay, resulting in the conversion of a neutron to a proton.
(b) Magnesium-22 has 10 neutrons and 12 protons, so N/Z = 0.83 (too low). Alternatively, you can look up the atomic mass of magnesium, which is 24.31 amu; a magnesium nuclide with a mass number of 22 is too light (the N/Z ratio is too low). Therefore, Mg-22 undergoes positron emission, resulting in the conversion of a proton to a neutron.(Electron
capture would accomplish the same thing as positron emission, but in Mg-22, positron emission is the only decay mode observed.)
(c) Molybdenum-102 has 60 neutrons and 42 protons, so N/Z = 1.43. However, for Z = 42, you can see from Figure 19.4 that stable nuclei should have an N/Z ratio of about 1.3. Alternatively, you can look up the atomic mass of molybdenum, which is 95.94 amu; a molybdenum nuclide with a mass number of 102 is too heavy to be stable (the N/Z ratio is too high). Therefore, Mo-102 undergoes beta decay, resulting in the conversion of a neutron to a proton.

FiguRe 19.4 Stable and unstable Nuclei A plot of N (the number of neutrons) versus Z (the number of protons) for all known stable nuclei—represented by green dots on this graph—shows that these nuclei cluster together in a region known as the valley (or island) of stability. Nuclei with an N/Z ratio that is too high tend to undergo beta decay. Nuclei with an N/Zratio that is too low tend to undergo positron emission or electron capture.