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Chapter 21: Problem 65

(a) Which of the following are required characteristics of an isotope to be used as a fuel in a nuclear power reactor? (i) It must emit gamma radiation. (ii) On decay, it must release two or more neutrons. (iii) It must have a half-life less than one hour. (iv) It must undergo fission upon the absorption of a neutron. (b) What is the most common fissionable isotope in a commercial nuclear power reactor?

Short Answer

Expert verified
In summary, the required characteristics for an isotope to be used as fuel in a nuclear power reactor are (ii) On decay, it must release two or more neutrons and (iv) It must undergo fission upon the absorption of a neutron. The most common fissionable isotope used in commercial nuclear power reactors is Uranium-235 (\(^{235}\)U).

Step by step solution

01

Part (a)

We will now examine each of the given statements: (i) It must emit gamma radiation. Gamma radiation is not a requirement for an isotope to be considered fuel in a nuclear power reactor. Gamma radiation is a byproduct of the fission process, but it is not necessary for the isotope to emit it in order to be used as fuel. (ii) On decay, it must release two or more neutrons. This is a requirement for an isotope to be used as fuel in a nuclear power reactor. When a nucleus undergoes fission, it produces smaller nuclei and neutrons which are utilized to sustain a controlled chain reaction. Two or more neutrons must be released in order to maintain a continuous chain reaction. (iii) It must have a half-life less than one hour. A short half-life is not a requirement for an isotope to be used as fuel in a nuclear power reactor. In fact, having a short half-life may not be practical as it would require frequent refueling. Isotopes with longer half-lives are more suitable for use as nuclear fuel, as they can provide stable and sustained power production. (iv) It must undergo fission upon the absorption of a neutron. This is another requirement for an isotope to be used as fuel in a nuclear power reactor. When an isotope absorbs a neutron, it should undergo fission, leading to the release of energy and additional neutrons, which will continue the chain reaction. Hence, statements (ii) and (iv) are the required characteristics for an isotope to be used as fuel in a nuclear power reactor.
02

Part (b)

The most common fissionable isotope used in commercial nuclear power reactors is Uranium-235 (\(^{235}\)U). It is the primary fuel used in nuclear reactors, as it readily undergoes fission upon the absorption of a neutron, producing energy and sustaining the chain reaction necessary for power generation.

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Most popular questions from this chapter

Decay of which nucleus will lead to the following products: (a) bismuth- 211 by beta decay; (b) chromium 50 by positron emission; (c) tantalum-179 by electron capture; (d) radium-226 by alpha decay?

Indicate the number of protons and neutrons in the following nuclei: (a) \({ }_{53}^{129} \mathrm{I}\), (b) \({ }^{138} \mathrm{Ba}\), (c) neptunium-237.

A rock contains \(0.257 \mathrm{mg}\) of lead-206 for every milligram of uranium-238. The half-life for the decay of uranium-238 to lead-206 is \(4.5 \times 10^{5} \mathrm{yr}\). How old is the rock? SOLUTION Analyze We are told that a rock sample has a certain amount of lead206 for every unit mass of uranium-238 and asked to estimate the age of the rock. Plan Lead-206 is the product of the radioactive decay of uranium-238. We will assume that the only source of lead-206 in the rock is from the decay of uranium-238, with a known half-life. To apply firstorder kinetics expressions (Equations \(21.19\) and 21.20) to calculate the time elapsed since the rock was formed, we first need to calculate how much initial uranium-238 there was for every \(1 \mathrm{mg}\) that remains today. Solve Let's assume that the rock currently contains \(1.000 \mathrm{mg}\) of uranium-238 and therefore \(0.257 \mathrm{mg}\) of lead-206. The amount of uranium-238 in the rock when it was first formed therefore equals \(1.000 \mathrm{mg}\) plus the quantity that has decayed to lead-206. Because the mass of lead atoms is not the same as the mass of uranium atoms, we cannot just add \(1.000 \mathrm{mg}\) and \(0.257 \mathrm{mg}\). We have to multiply the present mass of lead-206 \((0.257 \mathrm{mg})\) by the ratio of the mass number of uranium to that of lead, into which it has decayed. Therefore, the original mass of \({ }_{92}^{239} \mathrm{U}\) was $$ \text { Original } \begin{aligned} { }_{98}^{238} \mathrm{U} &=1.000 \mathrm{mg}+\frac{238}{206}(0.257 \mathrm{mg}) \\ &=1.297 \mathrm{mg} \end{aligned} $$ Using Equation 21.20, we can calculate the decay constant for the process from its half-life: $$ k=\frac{0.693}{4.5 \times 10^{9} \mathrm{yr}}=1.5 \times 10^{-10} \mathrm{yr}^{-1} $$ Rearranging Equation \(21.19\) to solve for time, \(t\), and substituting known quantities gives $$ t=-\frac{1}{k} \ln \frac{N_{t}}{N_{0}}=-\frac{1}{1.5 \times 10^{-10} \mathrm{yr}^{-1}} \ln \frac{1.000}{1.297}=1.7 \times 10^{9} \mathrm{yr} $$ Comment To check this result, you could use the fact that the decay of uranium-235 to lead-207 has a half-life of \(7 \times 10^{8} \mathrm{yr}\) and measure the relative amounts of uranium-235 and lead-207 in the rock.

Write balanced nuclear equations for the following processes: (a) rubidium-90 undergoes beta emission; (b) selenium-72 undergoes electron capture; (c) krypton- 76 undergoes positron emission; (d) radium-226 emits alpha radiation.

One of the nuclides in each of the following pairs is radioactive. Predict which is radioactive and which is stable: (a) \({ }_{19}^{39} \mathrm{~K}\) and \({ }_{19}^{40} \mathrm{~K}\), (b) \({ }^{209} \mathrm{Bi}\) and \({ }^{208} \mathrm{Bi}\), (c) nickel-58 and nickel-65.
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