Log out Go to App
Go to App

Learning Materials

Features

Discover

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: \({ }^{10} \mathrm{~B} + { }^1 \mathrm{n} \rightarrow { }^{11} \mathrm{~B} \rightarrow { }^{11} \mathrm{~C} + { }^{-1} \mathrm{e} + \bar{\nu}_\mathrm{e} \rightarrow { }^{11} \mathrm{~N} + { }^{-1} \mathrm{e} + \bar{\nu}_\mathrm{e}\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In a year, an average American uses about \(3 \times 10^{11} \mathrm{~J}\) of energy. How much mass does this translate to via \(E=m c^{2} ?\) Rock has a density approximately 3 times that of water, translating to about \(3 \mathrm{mg}\) per cubic millimeter. So roughly how big would a chunk of rock material be to provide a year's worth of energy if converted to pure energy? Is it more like dust, a grain of sand, a pebble, a rock, a boulder, a hill, a mountain?

Since each nuclear plant delivers \(\sim 1 \mathrm{GW}\) of electrical power, at \(\sim 40 \%\) thermodynamic efficiency this means a thermal generation rate of \(2.5\) GW. How many nuclear plants would we need to supply all 18 TW of our current energy demand? Since a typical lifetime is 50 years before decommissioning, how many days, on average would it be between new plants coming online (while old ones are retired) in a steady state?

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?

Operating approximately 450 nuclear plants over about 60 years at a total thermal level of \(1 \mathrm{TW}\), we have had two major radioactive releases into the environment. If we went completely down the nuclear road and get all \(18 \mathrm{TW}^{89}\) this way, what rate of accidents might we expect, if the rate just scales with usage levels?

Based on the calculation that 18 TW would require an annual cube of seawater \(300 \mathrm{~m}\) on a side to provide enough deuterium, what is your personal share as one of 8 billion people on earth, in liters? Could you lift this yourself? One cubic meter is \(1,000 \mathrm{~L}\).
See all solutions

Recommended explanations on Environmental Science Textbooks

Biological Resources

Read Explanation

Ecological Conservation

Read Explanation

Physical Environment

Read Explanation

Ecology Research

Read Explanation

Sustainability

Read Explanation

Pollution

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free