Chapter 21

Indicate the number of protons and neutrons in the following nuclei: \((\mathbf{a}){ }_{94}^{239} \mathrm{Pu},(\mathbf{b}){ }^{142} \mathrm{Ba},(\mathbf{c})\) potassium- 41 .

Indicate the number of protons and neutrons in the following nuclei: (a)\({ }_{83}^{214} \mathrm{Bi}\) (b) \({ }_{82}^{210} \mathrm{~Pb}\), (c) uranium-235.

Write balanced nuclear equations for the following processes: (a) radon-198 undergoes alpha emission; (b) thorium-234 undergoes beta emission; (c) copper-61 undergoes positron emission; (d) silver-106 undergoes electron capture.

Write balanced nuclear equations for the following transformations: (a) polonium-210 emits alpha particle; (b) neptunium-235 undergoes electron capture; (c) fluorine-18 emits beta particle; (d) carbon-14 decays by beta emission.

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

What particle is produced during the following decay processes: (a) actinium-215 decays to francium-211; (b) boron-13 decays to carbon-13; (c) holmium-151 decays to terbium-147; (d) carbon-11 decays to boron-11?

The naturally occurring radioactive decay series that begins with \({ }_{92}^{235} \mathrm{U}\) stops with formation of the stable \({ }_{82}^{207} \mathrm{~Pb}\) nucleus. The decays proceed through a series of alpha-particle and beta-particle emissions. How many of each type of emission are involved in this series?

A radioactive decay series that begins with \({ }_{90}^{232}\) Th ends with formation of the stable nuclide \({ }_{82}^{208} \mathrm{~Pb} .\) How many alpha-particle emissions and how many beta-particle emissions are involved in the sequence of radioactive decays?

Predict the type of radioactive decay process for the following radionuclides: (a) \({ }_{8}^{15} \mathrm{O}\) (b) \({ }_{21}^{41} \mathrm{Sc}\) (c) uranium-237, (d) sulphur-35.

Each of the following nuclei undergoes either beta decay or positron emission. Predict the type of emission for each: (a) \(\frac{90}{38} \mathrm{Sr},(\mathbf{b})_{38}^{85} \mathrm{Sr}\) (c) potassium-40, (d) sulfur-30.

One of the nuclides in each of the following pairs is radioactive. Predict which is radioactive and which is stable: (a) \(\frac{92}{44} \mathrm{Ru}\) and \({ }^{102} \mathrm{Ru}\), (b) \({ }_{56}^{138} \mathrm{Ba}\) and \({ }^{139} \mathrm{Ba}\) (c) tin-109 and \(\operatorname{tin}-120\)

One nuclide in each of these pairs is radioactive. Predict which is radioactive and which is stable: \((\mathbf{a}){ }_{20}^{40} \mathrm{Ca}\) and \({ }_{20}^{45} \mathrm{Ca},\) (b) \(^{12} \mathrm{C}\) and \({ }^{14} \mathrm{C}\) (c) lead-206 and thorium-230. Explain your choice in each case.

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.

Which of the following nuclides would you expect to be radioactive: \({ }_{26}^{58} \mathrm{Fe},{ }_{27}^{60} \mathrm{Co},{ }_{41}^{92} \mathrm{Nb},\) mercury-202, radium-226? Justify your choices.

Which statement best explains why nuclear transmutations involving neutrons are generally easier to accomplish than those involving protons or alpha particles? (a) Neutrons are not a magic number particle. (b) Neutrons do not have an electrical charge. (c) Neutrons are smaller than protons or alpha particles. (d) Neutrons are attracted to the nucleus even at long distances, whereas protons and alpha particles are repelled.

In 1930 the American physicist Ernest Lawrence designed the first cyclotron in Berkeley, California. In 1937 Lawrence bombarded a molybdenum target with deuterium ions, producing for the first time an element not found in nature. What was this element? Starting with molybdenum-96 as your reactant, write a nuclear equation to represent this process.

Complete and balance the following nuclear equations by supplying the missing particle: (a) \({ }_{94}^{239} \mathrm{Pu}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{-1}^{0} \mathrm{e}+?\) (b) \({ }_{92}^{238} \mathrm{U}+{ }_{2}^{4} \mathrm{He} \longrightarrow 3{ }_{0}^{1} \mathrm{n}+?\) (c) \({ }^{218} \mathrm{At} \longrightarrow{ }_{-1}^{0} \mathrm{e}+?\) (d) \({ }_{62}^{146} \mathrm{Sm} \longrightarrow{ }_{60}^{142} \mathrm{Nd}+?\) (e) \({ }_{53}^{118} \mathrm{I}+{ }_{-1}^{0} \mathrm{e} \longrightarrow\) ?

Complete and balance the following nuclear equations by supplying the missing particle: (a) \({ }_{47}^{106} \mathrm{Ag}+{ }_{-1}^{0} \mathrm{e} \longrightarrow ?\) (b) \({ }_{106}^{263} \mathrm{Sg} \longrightarrow{ }_{2}^{4} \mathrm{He}+?\) (c) \({ }_{84}^{216} \mathrm{Po} \longrightarrow{ }_{82}^{212} \mathrm{~Pb}+?\) (d) \({ }_{5}^{10} \mathrm{~B}+? \longrightarrow{ }_{3}^{7} \mathrm{Li}+{ }_{2}^{4} \mathrm{He}\) (e) \({ }_{86}^{220} \mathrm{Rn} \longrightarrow{ }_{2}^{4} \mathrm{He}+?\)

Write balanced equations for each of the following nuclear reactions: \((\mathbf{a}){ }_{92}^{238} \mathrm{U}(\mathrm{n}, \gamma){ }^{239} \mathrm{U},(\mathbf{b}){ }_{8}^{16} \mathrm{O}(\mathrm{p}, \alpha){ }^{13} \mathrm{~N},\) (c) \({ }_{8}^{18} \mathrm{O}\left(\mathrm{n}, \beta^{-}\right){ }_{9}^{19} \mathrm{~F} .\)

Each statement that follows refers to a comparison between two radioisotopes, A and X. Indicate whether each of the following statements is true or false. (a) If the half-life for \(\mathrm{A}\) is shorter than the half-life for \(\mathrm{X}, \mathrm{A}\) has a larger decay rate constant. (b) If \(\mathrm{X}\) is "not radioactive," its half-life is essentially zero. (c) If A has a half-life of 10 yr, and \(X\) has a half-life of \(10,000 \mathrm{yr}\), A would be a more suitable radioisotope to measure processes occurring on the 40 -yr time scale.

Some watch dials are coated with a phosphor, like \(\mathrm{ZnS}\), and a polymer in which some of the \({ }^{1} \mathrm{H}\) atoms have been replaced by \({ }^{3} \mathrm{H}\) atoms, tritium. The phosphor emits light when struck by the beta particle from the tritium decay, causing the dials to glow in the dark. The half-life of tritium is 12.3 yr. If the light given off is assumed to be directly proportional to the amount of tritium, by how much will a dial be dimmed in a watch that is 50 yr old?

It takes 180 minutes for a 200 -mg sample of an unknown radioactive substance to decay to \(112 \mathrm{mg}\). What is the halflife of this substance?

How much time is required for a 5.00-g sample of \({ }^{233} \mathrm{~Pa}\) to decay to \(0.625 \mathrm{~g}\) if the half-life for the beta decay of \({ }^{233} \mathrm{~Pa}\) is 27.4 days?

A 10.00 -g plant fossil from an archaeological site is found to have \(\mathrm{a}^{14} \mathrm{C}\) 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?

A wooden artifact from an Indian temple has a \({ }^{14} \mathrm{C}\) activity of 42 counts per minute as compared with an activity of 58.2 counts per minute for a standard zero age. From the half-life of \({ }^{14} \mathrm{C}\) decay, 5715 years, calculate the age of the artifact.

Phosphorus-32 is commonly used in nuclear medicine for the identification of malignant tumors. It decays to sulphur-32 with a half-life of 14.29 days. If a patient is given \(3.5 \mathrm{mg}\) of phosphorus- \(32,\) how much phosphorus-32 will remain after 1 month (i.e. 30 days)?

Iodine-131 is used as a nuclear medicine to treat hyperthyroidism. The half- life of \({ }^{131}\) I is 8.04 days. How long will it take for a \(500 \mathrm{mg}\) sample of \({ }^{131}\) I to decay into \(1 \%\) of its original mass?

An analytical laboratory balance typically measures mass to the nearest \(0.1 \mathrm{mg}\). What energy change would accompany the loss of \(0.1 \mathrm{mg}\) in mass?

The energy from solar radiation falling on Earth is \(1.07 \times 10^{16} \mathrm{~kJ} / \mathrm{min} .(\mathbf{a})\) How much loss of mass from the Sun occurs in one day from just the energy falling on Earth? (b) If the energy released in the reaction $$ { }^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{56}^{141} \mathrm{Ba}+{ }_{36}^{92} \mathrm{Kr}+3{ }_{0}^{1} \mathrm{n} $$ \(\left(\begin{array}{c}235 \\ \mathrm{U} \text { nuclear mass, } 234.9935 \mathrm{u} ;{ }^{141} \mathrm{Ba} \text { nuclear mass, }\end{array}\right.\) \(140.8833 \mathrm{u} ;{ }^{92} \mathrm{Kr}\) nuclear mass, \(91.9021 \mathrm{u}\) ) is taken as typical of that occurring in a nuclear reactor, what mass of uranium- 235 is required to equal \(0.10 \%\) of the solar energy that falls on Earth in 1.0 day?

Iodine-131 is a convenient radioisotope to monitor thyroid activity in humans. It is a beta emitter with a half-life of 8.02 days. The thyroid is the only gland in the body that uses iodine. A person undergoing a test of thyroid activity drinks a solution of NaI, in which only a small fraction of the iodide is radioactive. (a) Why is NaI a good choice for the source of iodine? (b) If a Geiger counter is placed near the person's thyroid (which is near the neck) right after the sodium iodide solution is taken, what will the data look like as a function of time? (c) A normal thyroid will take up about \(12 \%\) of the ingested iodide in a few hours. How long will it take for the radioactive iodide taken up and held by the thyroid to decay to \(0.01 \%\) of the original amount?

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?

(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?

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 \({ }^{238} \mathrm{U}\).

What is the function of the control rods in a nuclear reactor? What substances are used to construct control rods? Why are these substances chosen?

(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?

Complete and balance the nuclear equations for the following fission reactions: (a) \({ }_{94}^{239} \mathrm{Pu}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{52}^{137} \mathrm{Te}+{ }_{42}^{100} \mathrm{Mo}+\) (b) \({ }_{100}^{256} \mathrm{Fm}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{46}^{113} \mathrm{Pd}+{ }_{-}+4{ }_{0}^{1} \mathrm{n}\)

Which type or types of nuclear reactors have these characteristics? (a) Does not use a secondary coolant (b) Creates more fissionable material than it consumes (c) Uses a gas, such as He or \(\mathrm{CO}_{2}\), as the primary coolant

Hydroxyl radicals can pluck hydrogen atoms from molecules (“hydrogen abstraction"), and hydroxide ions can pluck protons from molecules ("deprotonation"). Write the reaction equations and Lewis dot structures for the hydrogen abstraction and deprotonation reactions for the generic carboxylic acid \(\mathrm{R}-\mathrm{COOH}\) with hydroxyl radical and hydroxide ion, respectively. Why is hydroxyl radical more toxic to living systems than hydroxide ion?

Which are not classified as ionizing radiation: gamma rays, beta particles, radio waves used in radio and television, and infrared radiation from sun?

A laboratory rat is exposed to an alpha-radiation source whose activity is \(14.3 \mathrm{mCi}\). (a) What is the activity of the radiation in disintegrations per second? In becquerels? (b) The rat has a mass of \(385 \mathrm{~g}\) and is exposed to the radiation for \(14.0 \mathrm{~s}\), absorbing \(35 \%\) of the emitted alpha particles, each having an energy of \(9.12 \times 10^{-13} \mathrm{~J} .\) Calculate the absorbed dose in millirads and grays. (c) If the RBE of the radiation is \(9.5,\) calculate the effective absorbed dose in mrem and Sv.

A \(65-\mathrm{kg}\) person is accidentally exposed for \(240 \mathrm{~s}\) to 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. (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 \((3 \mathrm{mSv}) ?\)

Chlorine has two stable nuclides, \({ }^{35} \mathrm{Cl}\) and \({ }^{37} \mathrm{Cl}\). In contrast, \({ }^{36} \mathrm{Cl}\) is a radioactive nuclide that decays by beta emission. (a) What is the product of decay of \({ }^{36} \mathrm{Cl}\) ? (b) Based on the empirical rules about nuclear stability, explain why the nucleus of \({ }^{36} \mathrm{Cl}\) is less stable than either \({ }^{35} \mathrm{Cl}\) or \({ }^{37} \mathrm{Cl}\).

When two protons fuse in a star, the product is \({ }^{2} \mathrm{H}\) plus a positron. Write the nuclear equation for this process.

Each of the following transmutations produces a radionuclide used in positron emission tomography (PET). (a) In equations (i) and (ii), identify the species signified as "X." (b) In equation (iii), one of the species is indicated as "d." What do you think it represents? (i) \({ }^{14} \mathrm{~N}(\mathrm{p}, \alpha) \mathrm{X}\) (ii) \({ }^{18} \mathrm{O}(\mathrm{p}, \mathrm{X})^{18} \mathrm{~F}\) (iii) \({ }^{14} \mathrm{~N}(\mathrm{~d}, \mathrm{n})^{15} \mathrm{O}\)

The nuclear masses of \({ }^{7} \mathrm{Be},{ }^{9} \mathrm{Be},\) and \({ }^{10} \mathrm{Be}\) are 7.0147,9.0100 , and \(10.0113 \mathrm{u}\), respectively. Which of these nuclei has the largest binding energy per nucleon?

A \(26.00-g\) sample of water containing tritium, \({ }_{1}^{3} \mathrm{H},\) emits \(1.50 \times 10^{3}\) beta particles per second. Tritium is a weak beta emitter with a half-life of 12.3 yr. What fraction of all the hydrogen in the water sample is tritium?

The Sun radiates energy into space at the rate of \(3.9 \times 10^{26} \mathrm{~J} / \mathrm{s} .\) (a) Calculate the rate of mass loss from the Sun in \(\mathrm{kg} /\) s. (b) How does this mass loss arise? (c) It is esti- mated that the Sun contains \(9 \times 10^{56}\) free protons. How many protons per second are consumed in nuclear reactions in the Sun?

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 0.53-g sample of fludeoxyglucose \(\left(\mathrm{C}_{6} \mathrm{H}_{11} \mathrm{FO}_{5}\right)\) contains radioactive fluorine- 18 (whose atomic mass is \(18.0 \mathrm{u}\) ). If \(68.3 \%\) of the fluorine atoms in the sample are fluorine-18 and the remainder are naturally occurring nonradioactive fluorine-19 atoms, how many disintegrations per second are produced by this sample? The half-life of fluorine- 18 is 110 min.

Charcoal samples from Stonehenge in England were burned in \(\mathrm{O}_{2}\), and the resultant \(\mathrm{CO}_{2}\) gas bubbled into a solution of \(\mathrm{Ca}(\mathrm{OH})_{2}\) (limewater), resulting in the precipitation of \(\mathrm{CaCO}_{3}\). The \(\mathrm{CaCO}_{3}\) was removed by filtration and dried. A 788-mg sample of the \(\mathrm{CaCO}_{3}\) had a radioactivity of \(1.5 \times 10^{-2} \mathrm{~Bq}\) due to carbon-14. By comparison, living organisms undergo 15.3 disintegrations per minute per gram of carbon. Using the half- life of carbon-14, 5700 yr, calculate the age of the charcoal sample.