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Chapter 21: Problem 64

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?

Short Answer

Expert verified
(a) The spent fuel elements are more radioactive because the fission products have a higher neutron-to-proton ratio, making them unstable and prone to radioactive decay, falling outside the belt of stability. (b) Beta-minus decay is 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 doesn't significantly change the neutron-to-proton ratio.

Step by step solution

01

Explain the radioactivity concerning the belt of stability

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.
02

Determine the dominant decay types based on the number of neutrons released per fission event

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.
03

Conclusion

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Belt of Stability
The belt of stability is an important concept when studying radioactive decay and nuclear stability. Imagine a chart that plots protons on one axis and neutrons on the other. This "belt" is a narrow strip where stable nuclei reside. If an atomic nucleus is on this belt, it means the atom has a balanced neutron to proton ratio and remains stable over time.

However, if a nucleus falls off this belt, becoming either too heavy or too light in terms of its neutron-to-proton ratio, it will be unstable. To reach stability, such nuclei often undergo radioactive decay, trying to adjust their ratio. This is why, after a fission reaction, the resulting fission products are much more unstable compared to the original fuel.
  • Nuclei outside the belt tend to undergo decay processes.
  • The goal of the decay is to reach a position on or closer to the belt, thereby achieving stability.
  • The "original fuel" in reactors aligns closer to this belt, while the fission products often lie well outside.
Fission Products
When a heavy nucleus splits during nuclear fission, the resulting fragments are called fission products. These products possess different characteristics compared to the original nucleus.

During the process, the heavy nucleus absorbs a neutron, becomes unstable, and splits into two lighter nuclei alongside a few neutrons. These newly formed nuclei often have a higher neutron-to-proton ratio compared to stable isotopes鈥攑lacing them outside the belt of stability.
  • Fission products are typically more neutron rich (high neutron-to-proton ratio).
  • These products are less stable and thus more radioactive.
  • Resulting instability leads to subsequent radioactive decays to achieve stability.
Understanding these products helps in predicting the types of radioactive decay, which in turn provides insights into nuclear waste management and safety protocols.
Heavy Nucleus
A heavy nucleus is one which contains a large number of protons and neutrons. Nuclei like uranium and plutonium fall under this category and are commonly used in nuclear reactors.

What makes these nuclei special is their tendency to undergo fission, a process where they split into smaller parts, releasing energy. This is largely due to their neutron-to-proton ratio, which is higher than that of lighter, more stable nuclei.
  • Heavy nuclei have a higher neutron-to-proton ratio.
  • This imbalance leads to instability, making them ideal candidates for fission reactions.
  • Fission of such nuclei not only produces energy but also results in radioactive fission products.
These heavy elements play a crucial role in nuclear power generation, but their radioactivity and the resulting fission products necessitate careful handling and disposal.

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Most popular questions from this chapter

(a) What is the function of the moderator in a nuclear reactor? (b) What substance acts as the moderator in a pressurized water generator? (c) What other substances are used as a moderator in nuclear reactor designs?

Which of the following statements best explains why alpha emission is relatively common, but proton emission is extremely rare? (a) Alpha particles are very stable because of magic numbers of protons and neutrons. (b) Alpha particles occur in the nucleus. (c) Alpha particles are the nuclei of an inert gas. (d) An alpha particle has a higher charge than a proton.

The isotope \({ }_{28}^{62} \mathrm{Ni}\) has the largest binding energy per nucleon of any isotope. Calculate this value from the atomic mass of nickel-62 \((61.928345 \mathrm{u})\) and compare it with the value given for iron- 56 in Table 21.7 .

Despite the similarities in the chemical reactivity of elements in the lanthanide series, their abundances in Earth's crust vary by two orders of magnitude. This graph shows the relative abundance as a function of atomic number. Which of the following statements best explains the sawtooth variation across the series? (a) The elements with an odd atomic number lie above the belt of stability. (b) The elements with an odd atomic number lie below the belt of stability. (c) The elements with an even atomic number have a magic number of protons. (d) Pairs of protons have a special stability.

Why is it important that radioisotopes used as diagnostic tools in nuclear medicine produce gamma radiation when they decay? Why are alpha emitters not used as diagnostic tools?
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