Chapter 21

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

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

What do these symbols stand for? (a) \({ }_{0}^{0} \gamma,(\mathbf{b}){ }_{2}^{4} \mathrm{He},\) (c) \({ }_{0}^{1} \mathrm{n} .\)

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: (a) uranium-235 by alpha decay; (b) aluminium-26 by positron emission; \((\mathbf{c})\) 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?

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

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

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 \({ }^{102} \mathrm{Ru},(\mathbf{b}){ }_{56}^{138} \mathrm{Ba}\) and \({ }_{56}^{139} \mathrm{Ba},(\mathbf{c})\) tin -109 and 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 nuclides have magic numbers of both protons and neutrons: \((\mathbf{a})\) beryllium- \(10,(\mathbf{b})\) silicon- 28 , (c) chromium-52, (d) nickel-56, (e) krypton-84?

Despite the similarities in the chemical reactivity of elements in the lanthanide series, their abundances in Earth's crust vary by two orders of magnitude. This graph shows the relative abundance as a function of atomic number. Which of the following statements best explains the sawtooth variation across the series? (a) The elements with an odd atomic number lie above the belt of stability. (b) The elements with an odd atomic number lie below the belt of stability. (c) The elements with an even atomic number have a magic number of protons. (d) Pairs of protons have a special stability.

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) \({ }_{47}^{106} \mathrm{Ag}+{ }_{-1}^{0} \mathrm{e} \longrightarrow ?\) (b) \({ }_{106}^{263} \mathrm{Sg} \longrightarrow{ }_{2}^{4} \mathrm{He}+?\) (c) \({ }_{84}^{216} \mathrm{Po} \longrightarrow{ }_{82}^{212} \mathrm{~Pb}+?\) (d) \({ }_{5}^{10} \mathrm{~B}+? \longrightarrow{ }_{3} \mathrm{Li}+{ }_{2}^{4} \mathrm{He}\) (e) \({ }^{220} \mathrm{Rn} \longrightarrow{ }_{2}^{4} \mathrm{He}+?\)

Write balanced equations for (a) \({ }_{92}^{238} \mathrm{U}(\alpha, \mathrm{n}){ }^{241} \mathrm{Pu},\) (b) \({ }^{14} \mathrm{~N}(\alpha, \mathrm{p}){ }^{17} \mathrm{O},(\mathbf{c}){ }_{26}^{56} \mathrm{Fe}\left(\alpha, \beta^{-}\right)_{29}^{60} \mathrm{Cu} .\)

Write balanced equations for each of the following nuclear reactions: \((\mathbf{a}){ }_{92}^{238} \mathrm{U}(\mathrm{n}, \gamma){ }^{239} \mathrm{U},(\mathbf{b}){ }_{82}^{16} \mathrm{O}(\mathrm{p}, \alpha){ }^{13} \mathrm{~N},\) (c) \({ }_{8}^{18} \mathrm{O}\left(\mathrm{n}, \beta^{-}\right){ }^{19} \mathrm{~F}\).

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 \(X\) 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.

It has been suggested that strontium-90 (generated by nuclear testing) deposited in the hot desert will undergo radioactive decay more rapidly because it will be exposed to much higher average temperatures. (a) Is this a reasonable suggestion? (b) Does the process of radioactive decay have an activation energy, like the Arrhenius behavior of many chemical reactions (Section 14.5\() ?\)

Some watch dials are coated with a phosphor, like 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?

Cobalt-60 is a strong gamma emitter that has a half-life of \(5.26 \mathrm{yr}\). The cobalt- 60 in a radiotherapy unit must be replaced when its radioactivity falls to \(75 \%\) of the original sample. If an original sample was purchased in June \(2016,\) when will it be necessary to replace the cobalt- \(60 ?\)

How much time is required for a \(5.00-g\) sample of \({ }^{233}\) 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 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 nas a ' 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 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 \({ }^{131} \mathrm{I}\) is 8.04 days. How long will it take for a \(500 \mathrm{mg}\) sample of \({ }^{131} \mathrm{I}\) to decay into \(1 \%\) of its original mass?

The thermite reaction, \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Al}(s) \longrightarrow 2 \mathrm{Fe}(s)+\) \(\mathrm{Al}_{2} \mathrm{O}_{3}(s), \Delta H^{\circ}=-851.5 \mathrm{~kJ} / \mathrm{mol}\), is one of the most exothermic reactions known. Because the heat released is sufficient to melt the iron product, the reaction is used to weld metal under the ocean. How much heat is released per mole of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) produced? How does this amount of thermal energy compare with the energy released when 2 mol of protons and 2 mol of neutrons combine to form 1 mol of alpha particles?

How much energy must be supplied to break a single \({ }^{21}\) Ne nucleus into separated protons and neutrons if the nucleus has a mass of \(20.98846 \mathrm{u}\) ? What is the nuclear binding energy for \(1 \mathrm{~mol}\) of \({ }^{21} \mathrm{Ne}\) ?

The atomic masses of nitrogen-14, titanium- 48 , and xenon129 are \(13.999234 \mathrm{u}, 47.935878 \mathrm{u},\) and \(128.904779 \mathrm{u},\) respectively. For each isotope, calculate (a) the nuclear mass, (b) the nuclear binding energy, (c) the nuclear binding energy per nucleon.

The energy from solar radiation falling on Earth is \(1.07 \times 10^{16} \mathrm{~kJ} / \mathrm{min} .\) (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 $$ { }^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{56}^{141} \mathrm{Ba}+{ }_{36}^{92} \mathrm{Kr}+3{ }_{0}^{1} \mathrm{n} $$ \(\left({ }^{235} \mathrm{U}\right.\) nuclear mass, \(234.9935 \mathrm{u} ;{ }^{141} \mathrm{Ba}\) nuclear mass, \(140.8833 \mathrm{u} ;{ }^{92} \mathrm{Kr}\) 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?

The isotope \({ }_{28}^{62} \mathrm{Ni}\) has the largest binding energy per nucleon of any isotope. Calculate this value from the atomic mass of nickel-62 \((61.928345 \mathrm{u})\) and compare it with the value given for iron- 56 in Table 21.7 .

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 or fusion reactions: (a) \({ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{36}^{92} \mathrm{Kr}+{ }_{56}^{141} \mathrm{Zn}+\) (b) \({ }_{1}^{2} \mathrm{H}+{ }_{1}^{3} \mathrm{H} \longrightarrow{ }_{2}^{4} \mathrm{He}+\)

Complete and balance the nuclear equations for the following fission reactions: (a) \({ }_{99}^{239} \mathrm{Pu}+{ }_{0} \mathrm{n} \longrightarrow{ }_{52}^{137} \mathrm{Te}+{ }_{42}^{100} \mathrm{Mo}+\) (b) \({ }_{100}^{256} \mathrm{Fm}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{46}^{113} \mathrm{Pd}+{ }_{-}+4{ }_{0}^{1} \mathrm{n}\)

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.

The spent fuel elements from a fission reactor are much more intensely radioactive than the original fuel elements. (a) What does this tell you about the products of the fission process in relationship to the belt of stability, Figure \(21.2 ?(\mathbf{b})\) Given that only two or three neutrons are released per fission event and knowing that the nucleus undergoing fission has a neutron-to-proton ratio characteristic of a heavy nucleus, what sorts of decay would you expect to be dominant among the fission products?

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 \(\mathrm{He}\) 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 \(\mathrm{a}\) 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 \((3 \mathrm{mSv}) ?\)