The spent fuel elements from a fission reactor are much more intensely radioactive than the original fuel elements. (a) What does this tell you about the products of the fission process in relationship to the belt of stability, Figure \(21.2 ?(\mathbf{b})\) Given that only two or three neutrons are released per fission event and knowing that the nucleus undergoing fission has a neutron-to-proton ratio characteristic of a heavy nucleus, what sorts of decay would you expect to be dominant among the fission products?

The belt of stability is a region on a chart where stable atomic nuclei are found. It displays the relationship between the number of protons and neutrons in a stable nucleus. Nuclei that lie outside the belt of stability are considered unstable and undergo radioactive decay to achieve stability. Spent fuel elements from a fission reactor are more radioactive compared to the original fuel elements because the fission products, resulting from the splitting of heavy nuclei, usually have a higher neutron-to-proton ratio. These fission products fall outside the belt of stability, making them unstable and prone to radioactive decay.

When a fission event occurs in a heavy nucleus, two or three neutrons are released, and the resulting products will most likely have a neutron-to-proton ratio similar to the parent nucleus. For heavy nuclei, the neutron-to-proton ratio is greater than 1, which puts these nuclei above the belt of stability. Now, we need to analyze the possible decay types: alpha decay, beta decay, and gamma decay. (a) Alpha decay involves the loss of an alpha particle, which consists of 2 protons and 2 neutrons. However, this type of decay doesn't result in a significant change to the neutron-to-proton ratio of the fission products. (b) Beta decay involves the conversion of a neutron into a proton (beta-minus decay) or a proton into a neutron (beta-plus decay). Given that the neutron-to-proton ratio for heavy nuclei is greater than 1, it indicates that the heavy nucleus has more neutrons than required for stability. So, we can expect beta-minus decay to be more common, as it reduces the neutron-to-proton ratio. (c) Gamma decay involves the release of energy in the form of gamma photons. This type of decay doesn't change the neutron-to-proton ratio but often accompanies other decay types.

Based on the above analysis: (a) The increased radioactivity of spent fuel elements is due to the fission products having a higher neutron-to-proton ratio, which makes them unstable and more radioactive. (b) Beta-minus decay is expected to be the dominant decay type among fission products, as it reduces the neutron-to-proton ratio, moving the fission products towards the belt of stability. Gamma decay often accompanies other decay types, but it doesn't significantly change the neutron-to-proton ratio.