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Chapter 21: Problem 58

Which of the following statements about the uranium used in nuclear reactors is or are true? (i) Natural uranium has too little \({ }^{235} \mathrm{U}\) to be used as a fuel. (ii) \({ }^{238} \mathrm{U}\) cannot be used as a fuel because it forms a supercritical mass too easily. (iii) To be used as fuel, uranium must be enriched so that it is more than \(50 \%^{235} \mathrm{U}\) in composition. (iv) The neutron-induced fission of \({ }^{235} \mathrm{U}\) releases more neutrons per nucleus than fission of \({ }^{238} \mathrm{U}\)

Short Answer

Expert verified
The true statements about uranium used in nuclear reactors are (i) Natural uranium has too little \({ }^{235} \mathrm{U}\) to be used as a fuel, and (iv) The neutron-induced fission of \({ }^{235} \mathrm{U}\) releases more neutrons per nucleus than fission of \({ }^{238} \mathrm{U}\).

Step by step solution

01

Statement (i)

Natural uranium has too little \({ }^{235} \mathrm{U}\) to be used as a fuel. This statement is true. Natural uranium consists of around 0.72% of the isotope \({ }^{235} \mathrm{U}\) and about 99.3% of the isotope \({ }^{238} \mathrm{U}\). The \({ }^{235} \mathrm{U}\) isotope is significantly more fissionable than \({ }^{238} \mathrm{U}\), so its small proportion in natural uranium makes it insufficient for use as fuel in nuclear reactors without further processing.
02

Statement (ii)

\({ }^{238} \mathrm{U}\) cannot be used as a fuel because it forms a supercritical mass too easily. This statement is false. \({ }^{238} \mathrm{U}\) is not as fissionable as \({ }^{235} \mathrm{U}\), and it does not easily form a supercritical mass. In fact, \({ }^{238} \mathrm{U}\) requires a significant amount of energy input (such as fast-moving neutrons) to initiate fission, while \({ }^{235} \mathrm{U}\) can undergo fission with slow-moving (thermal) neutrons.
03

Statement (iii)

To be used as fuel, uranium must be enriched so that it is more than \(50 \%^{235} \mathrm{U}\) in composition. This statement is false. The percentage of \({ }^{235} \mathrm{U}\) required in uranium for nuclear reactors varies depending on the type of reactor and the desired power output, but it is typically between 3% and 5%. Some reactors can even use natural uranium. It is important to note that weapons-grade uranium, used for nuclear weapons, is typically enriched to around 90% \({ }^{235} \mathrm{U}\).
04

Statement (iv)

The neutron-induced fission of \({ }^{235} \mathrm{U}\) releases more neutrons per nucleus than fission of \({ }^{238} \mathrm{U}\). This statement is true. The fission of \({ }^{235} \mathrm{U}\) releases more neutrons per nucleus (averaging around 2 to 3) compared to the fission of \({ }^{238} \mathrm{U}\) (which usually releases around 1 to 2 neutrons per nucleus). The additional neutrons released from \({ }^{235} \mathrm{U}\) fission contribute to sustaining a nuclear chain reaction more effectively. In conclusion, the true statements about uranium used in nuclear reactors are (i) and (iv).

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Most popular questions from this chapter

A 10.00 -g plant fossil from an archaeological site is found to have a ${ }^{14} \mathrm{C}$ activity of 3094 disintegrations over a period of ten hours. A living plant is found to have a \({ }^{14} \mathrm{C}\) activity of 9207 disintegrations over the same period of time for an equivalent amount of sample with respect to the total contents of carbon. Given that the half-life of \({ }^{14} \mathrm{C}\) is 5715 years, how old is the plant fossil?

Decay of which nucleus will lead to the following products: (a) uranium-235 by alpha decay; (b) aluminium-26 by positron emission; \((\mathbf{c})\) deuterium by alpha decay; (d) yttrium-90 by beta decay?

A \(65-\mathrm{kg}\) person is accidentally exposed for \(240 \mathrm{~s}\) to \(\mathrm{a}\) 15-mCi source of beta radiation coming from a sample of ${ }^{90}$ Sr. (a) What is the activity of the radiation source in disintegrations per second? In becquerels? (b) Each beta particle has an energy of \(8.75 \times 10^{-14} \mathrm{~J} .\) and \(7.5 \%\) of the radiation is absorbed by the person. Assuming that the absorbed radiation is spread over the person's entire body, calculate the absorbed dose in rads and in grays. \((\mathbf{c})\) If the RBE of the beta particles is \(1.0,\) what is the effective dose in mrem and in sieverts? (d) Is the radiation dose equal to, greater than, or less than that for a typical mammogram \((3 \mathrm{mSv}) ?\)

The average energy released in the fission of a single uranium- 235 nucleus is about \(3 \times 10^{-11} \mathrm{~J}\). If the conversion of this energy to electricity in a nuclear power plant is \(40 \%\) efficient, what mass of uranium- 235 undergoes fission in a year in a plant that produces 1000 megawatts? Recall that a watt is \(1 \mathrm{~J} / \mathrm{s}\).

A portion of the Sun's energy comes from the reaction $$ 4{ }_{1}^{1} \mathrm{H} \longrightarrow{ }_{2}^{4} \mathrm{He}+2{ }_{1}^{0} \mathrm{e} $$ which requires a temperature of \(10^{6}\) to \(10^{7} \mathrm{~K}\). Use the mass of the helium-4 nucleus given in Table 21.7 to determine how much energy is released per mol of hydrogen atoms.
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