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Chapter 15: Problem 10

Control rods in nuclear reactors tend to contain \({ }^{10} \mathrm{~B}\), which has a high neutron absorption cross section. \(^{81}\) What happens to this nucleus when it absorbs a neutron, and is the result stable? If not, track the decay chain until it lands on a stable nucleus.

Short Answer

Expert verified
Answer: The final stable nucleus is ${}^{11} \mathrm{~N}$.

Step by step solution

01

Write down the nuclear reaction after neutron absorption

When a \({ }^{10} \mathrm{~B}\) nucleus absorbs a neutron, we add the neutron to the existing nucleus to represent the new nucleus. In this case, it becomes \({ }^{11} \mathrm{~B}\). Hence, the initial nuclear reaction can be represented as follows: \({ }^{10} \mathrm{~B} + { }^1 \mathrm{n} \rightarrow { }^{11} \mathrm{~B}\)
02

Check the stability of the new nucleus

We need to verify whether the resulting \({ }^{11} \mathrm{~B}\) is a stable nucleus or not. Checking the stability, we find that \({ }^{11} \mathrm{~B}\) is actually unstable, undergoing beta decay.
03

Represent the beta decay for \({ }^{11} \mathrm{~B}\)

In beta decay, a neutron in the nucleus is converted to a proton, with the emission of an electron (more specifically, an electron plus an electron antineutrino). As a result, the atomic number increases, while the mass number remains the same. We write the beta decay for \({ }^{11} \mathrm{~B}\) as follows: \({ }^{11} \mathrm{~B} \rightarrow { }^{11} \mathrm{~C} + { }^{-1} \mathrm{e} + \bar{\nu}_\mathrm{e}\)
04

Check the stability of \({ }^{11} \mathrm{~C}\)

Now, the resulting nucleus is \({ }^{11} \mathrm{~C}\). We need to check if it is stable or not. If it is stable, we are done. But, in this case, we find that \({ }^{11} \mathrm{~C}\) is also unstable and undergoes beta decay as well.
05

Represent the beta decay for \({ }^{11} \mathrm{~C}\)

We repeat the process for beta decay. Writing the beta decay for \({ }^{11} \mathrm{~C}\), we get: \({ }^{11} \mathrm{~C} \rightarrow { }^{11} \mathrm{~N} + { }^{-1} \mathrm{e} + \bar{\nu}_\mathrm{e}\)
06

Check the stability of \({ }^{11} \mathrm{~N}\)

Now, we have reached \({ }^{11} \mathrm{~N}\), and we need to verify its stability. In this case, we find that \({ }^{11} \mathrm{~N}\) is a stable nucleus. Thus, we have reached a stable nucleus following the decay chain. In conclusion, the \({ }^{10} \mathrm{~B}\) nucleus undergoes the following decay chain after absorbing a neutron: \({ }^{10} \mathrm{~B} + { }^1 \mathrm{n} \rightarrow { }^{11} \mathrm{~B} \rightarrow { }^{11} \mathrm{~C} + { }^{-1} \mathrm{e} + \bar{\nu}_\mathrm{e} \rightarrow { }^{11} \mathrm{~N} + { }^{-1} \mathrm{e} + \bar{\nu}_\mathrm{e}\)

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Most popular questions from this chapter

On balance, considering the benefits and downsides of conventional nuclear fission, where do you come down in terms of support for either terminating, continuing, or expanding our use of this technology? Should we pursue breeder reactors at a large scale? Please justify your conclusion based on the things you consider to be most important.

The world uses energy at a rate of \(18 \mathrm{TW}\), amounting to almost \(6 \times 10^{20}\) J per year. What is the mass-equivalent \(^{83}\) of this amount of annual energy? What context can you provide for this amount of mass?

If a friend creates a nucleus whose half-life is 4 hours and gives it to you at noon, what is the probability that it will not have decayed by noon the following day?

Explain in some detail what happens if control rods are too effective at absorbing neutrons so that each fission event produces too few unabsorbed neutrons.

Cosmic rays impinging on our atmosphere generate radioactive \({ }^{14} \mathrm{C}\) from \({ }^{14} \mathrm{~N}\) nuclei. \(^{78}\) These \({ }^{14} \mathrm{C}\) atoms soon team up with oxygen to form \(\mathrm{CO}_{2}\), so that plants absorbing \(\mathrm{CO}_{2}\) from the air will have about one in a trillion of their carbon atoms in this form. Animals eating these plants \(^{79}\) will also have this fraction of carbon in their bodies, until they die and stop cycling carbon into their bodies. At this point, the fraction of carbon atoms in the form of \({ }^{14} \mathrm{C}\) in the body declines, with a half life of 5,715 years. If you dig up a human skull, and discover that only one-eighth of the usual one-trillionth of carbon atoms are \({ }^{14} \mathrm{C}\), how old do you deem the skull to be?
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