Chapter 25

Rank the three types of natural radiation \((\alpha, \beta, \gamma)\): (a) In order of increasing mass (b) In order of increasing penetrating power

Cobalt-60, used as a source of high-energy gamma radiation in medical procedures, is made in a nuclear reactor by neutron irradiation of cobalt-59. Write an equation for this reaction.

Explain why carbon-14 dating is limited to the range of 100 to about 60,000 years.

The uranium- 235 radioactive decay series includes 7 alpha emissions and 4 beta emissions. Identify the stable isotope at the end of this series.

The fission of uranium- 235 releases \(2 \times 10^{10} \mathrm{kJ} /\) mol. Calculate the quantity of mass converted to energy in this process.

In a nuclear reactor, what is a moderator and what is its function?

Identify the other element generated in the reaction \(^{235} \mathrm{U}+^{1} \mathrm{n} \rightarrow^{141} \mathrm{Ba}+2^{1} \mathrm{n}+?\)

What are the units associated with each of the following: (a) curie (b) rad

The interaction of radiation with matter has both positive and negative consequences. Discuss briefly the hazards of radiation and the way that radiation can be used in medicine.

What are the essential criteria for a radioactive isotope to be used for medical imaging?

Write equations that describe the preparation of technetium-99m from molybdenum-98.

Oxygen-15 is used in the medical procedure called positron emission tomography. This isotope is prepared on a cyclotron from irradiation of nitrogen-14 with deuterium nuclei. It decays to nitrogen-15 by positron emission, and the positrons are annihilated when they collide with electrons, forming two gamma rays. Write equations for the three reactions described here.

What are the advantages and disadvantages of food preservation using radiation?

Complete the following nuclear equations. Write the mass number and atomic number for the remaining particle, as well as its symbol. (a) \(^{54}_{26} \mathrm{Fe}+^{4}_{2} \mathrm{He} \longrightarrow 2 \frac{1}{0} \mathrm{n}+?\) (b) \(^{27}_{13} \mathrm{Al}+^{4}_{2} \mathrm{He} \longrightarrow_{15}^{30} \mathrm{P}+?\) (c) \(^{32}_{16} \mathrm{S}+^{1}_{0} \mathrm{n} \longrightarrow_{1}^{1} \mathrm{H}+?\) (d) \(_{42}^{96} \mathrm{Mo}+_{1}^{2} \mathrm{H} \longrightarrow_{0}^{1} \mathrm{n}+?\) (e) \(^{98}_{42} \mathrm{Mo}+^{1}_{0} \mathrm{n} \longrightarrow _{99}^{43} \mathrm{Tc}+?\) (f) \(^{18}_{9} \mathrm{F} \longrightarrow_{18}^{8} \mathrm{O}+?\)

The uranium- 235 radioactive decay series, beginning with \(^{235}_{92} \mathrm{U}\) and ending with \(^{207}_ {82} \mathrm{Pb}\) occurs in the following sequence: \(\alpha, \beta, \alpha, \beta, \alpha, \alpha, \alpha, \alpha, \beta, \beta, \alpha\) Write an equation for each step in this series.

The thorium- 232 radioactive decay series, beginning with \(^{232}_{90} \mathrm{TH}\) and ending with \(^{208}_{82} \mathrm{Pb}\) occurs in the following sequence: \(\alpha, \beta, \beta, \alpha, \alpha, \alpha, \alpha, \beta, \beta, \alpha\) Write an equation for each step in this series.

What particle is emitted in the following nuclear reactions? Write an equation for each reaction. (a) Gold-198 decays to mercury-198. (b) Radon-222 decays to polonium-218. (c) Cesium-137 decays to barium-137. (d) Indium- 110 decays to cadmium- 110 .

What is the product of the following nuclear decay processes? Write an equation for each process. (a) Gallium-67 decays by electron capture. (b) Potassium-38 decays with positron emission. (c) Technetium-99m decays with \(\gamma\) emission. (d) Manganese-56 decays by \(\beta\) emission.

Predict the probable mode of decay for each of the following radioactive isotopes, and write an equation to show the products of decay. (a) manganese- 54 (b) americium- 241 (c) silver-110 (d) mercury-197m

(a) Which of the following nuclei decay by \(-{ }_{1}^{0} \beta\) decay? \({ }^{3} \mathrm{H}^{16} \mathrm{O} \quad{ }^{20} \mathrm{~F} \quad{ }^{13} \mathrm{~N}\) (b) Which of the following nuclei decays by \({ }_{+1}^{0} \beta\) decay? \({ }^{238} \mathrm{U} \quad{ }^{19} \mathrm{~F} \quad{ }^{22} \mathrm{Na} \quad{ }^{24} \mathrm{Na}\)

(a) Which of the following nuclei decay by $$ -_{1}^{0} \beta \text { decay? } $$ $$^{1} \mathrm{H} \quad^{23} \mathrm{Mg} \quad^{32} \mathrm{P} \quad^{20} \mathrm{Ne}$$ (b) Which of the following nuclei decay by \(+_{1}^{0} \beta\) decay? $$^{235} \mathrm{U} \quad^{35} \mathrm{Cl} \quad^{38} \mathrm{K} \quad^{24} \mathrm{Na}$$

Calculate the binding energy per mole of nucleons for calcium- \(40,\) and compare your result with the value in Figure \(25.4 .\) Masses needed for this calculation are (in g/mol) \(_{1}^{1} \mathrm{H}=1.00783,_{0}^{1} \mathrm{n}=1.00867\) and \(_{20}^{40} \mathrm{Ca}=39.96259\)

Calculate the binding energy per mole of nucleons for iron-56. Masses needed for this calculation (in g/mol) are \(_{1}^{1} \mathrm{H}=1.00783,_{0}^{1} \mathrm{n}=1.00867,\) and \(\frac{56}{26} \mathrm{Fe}=55.9349 .\) Compare the result of your calculation to the value for iron-56 in the graph in Figure 25.4

Calculate the binding energy per mole of nucleons for \(_{8}^{16} \mathrm{O} .\) Masses needed for this calculation are \(_{1}^{1} \mathrm{H}=1.00783,_{0}^{1} \mathrm{n}=1.00867,\) and \(_{8}^{16} \mathrm{O}=15.99492\)

Copper(II) acetate containing \(^{64} \mathrm{Cu}\) is used to study brain tumors. This isotope has a half-life of 12.7 hours. If you begin with \(25.0 \mu \mathrm{g}\) of \(^{64} \mathrm{Cu},\) what mass remains after 63.5 hours?

Gold-198 is used in the diagnosis of liver problems. The half-life of \(^{198}\) Au is 2.69 days. If you begin with \(2.8 \mu \mathrm{g}\) of this gold isotope, what mass remains after 10.8 days?

Iodine-131 is used to treat thyroid cancer. (a) The isotope decays by \(\beta\) -particle emission. Write a balanced equation for this process. (b) Iodine-131 has a half-life of 8.04 days. If you begin with \(2.4 \mu \mathrm{g}\) of radioactive \(^{131} \mathrm{I},\) what mass remains after 40.2 days?

Phosphorus-32 is used in the form of \(\mathrm{Na}_{2} \mathrm{HPO}_{4}\) in the treatment of chronic myeloid leukemia, among other things. (a) The isotope decays by \(\beta\) -particle emission. Write a balanced equation for this process. (b) The half-life of \(^{32} \mathrm{P}\) is 14.3 days. If you begin with \(4.8 \mu \mathrm{g}\) of radioactive \(^{32} \mathrm{P}\) in the form of \(\mathrm{Na}_{2} \mathrm{HPO}_{4},\) what mass remains after 28.6 days (about 1 month)?

Gallium-67$$\left(t_{1 / 2}=78.25 \text { hours }\right)$$ is used in the medical diagnosis of certain kinds of tumors. If you ingest a compound containing 0.015 mg of this isotope, what mass (in milligrams) remains in your body after 13 days? (Assume none is excreted.)

Iodine-131 \(\left(t_{1 / 2}=8.04 \text { days }\right),\) a \(\beta\) emitter, is used to treat thyroid cancer. (a) Write an equation for the decomposition of \(^{131}\) I. (b) If you ingest a sample of NaI containing \(^{131}\) I, how much time is required for the activity to decrease to \(35.0 \%\) of its original value?

Radon has been the focus of much attention recently because it is often found in homes. Radon-222 emits \(\alpha\) particles and has a half-life of 3.82 days. (a) Write a balanced equation to show this process. (b) How long does it take for a sample of \(^{222} \mathrm{Rn}\) to decrease to \(20.0 \%\) of its original activity?

Strontium-90 is a hazardous radioactive isotope that resulted from atmospheric testing of nuclear weapons. A sample of strontium carbonate containing \(^{90}\) Sr is found to have an activity of \(1.0 \times 10^{3} \mathrm{dpm} .\) One year later, the activity of this sample is \(975 \mathrm{dpm} .\) (a) Calculate the half-life of strontium-90 from this information. (b) How long will it take for the activity of this sample to drop to \(1.0 \%\) of the initial value?

Radioactive cobalt-60 is used extensively in nuclear medicine as a \(\gamma\) -ray source. It is made by a neutron capture reaction from cobalt-59 and is a \(\beta\) emitter; \(\beta\) emission is accompanied by strong \(\gamma\) radiation. The half-life of cobalt-60 is 5.27 years. (a) How long will it take for a cobalt- 60 source to decrease to one eighth of its original activity? (b) What fraction of the activity of a cobalt-60 source remains after 1.0 year?

Scandium occurs in nature as a single isotope, scandium-45. Neutron irradiation produces scandium- \(46,\) a \(\beta\) emitter with a half-life of 83.8 days. If the initial activity is \(7.0 \times 10^{4} \mathrm{dpm},\) draw a graph showing disintegrations per minute as a function of time during a period of 1 year.

Americium-240 is made by bombarding plutonium-239 with \(\alpha\) particles. In addition to \(^{240} \mathrm{Am},\) the products are a proton and two neutrons. Write a balanced equation for this process.

There are two isotopes of americium, both with half-lives sufficiently long to allow the handling of large quantities. Americium-241, with a half-life of 432 years, is an \(\alpha\) emitter used in smoke detectors. The isotope is formed from \(^{239} \mathrm{Pu}\) by absorption of two neutrons followed by emission of a \(\beta\) particle. Write a balanced equation for this process.

The superheavy element \(^{287} \mathrm{Fl}\) (element 114 ) was made by firing a beam of \(^{48}\) Ca ions at \(^{242}\) Pu. Three neutrons were ejected in the reaction. Write a balanced nuclear equation for the synthesis of \(^{287} \mathrm{Fl}\).

To synthesize the heavier transuranium elements, a nucleus must be bombarded with a relatively large particle. If you know the products are californium- 246 and four neutrons, with what particle would you bombard uranium- 238 atoms?

Deuterium nuclei \(\left(_{1}^{2} \mathrm{H}\right)\) are particularly effective as bombarding particles to carry out nuclear reactions. ng equations: (a) \(^{114}_{48} \mathrm{Cd}+\\_{2}^{1} \mathrm{H} \longrightarrow ?+\\_{1}^{1} \mathrm{H}\) (b) \(_{3}^{6} \mathrm{Li}+\\_{2}^{1} \mathrm{H} \longrightarrow ?+\\_{1}^{0} \mathrm{n}\) (c) \(\\_{40}^{20} \mathrm{Ca}+\\_{2}^{1} \mathrm{H} \longrightarrow_{11}^{38} \mathrm{K}+?\) (d) \(?+\\_{2}^{1} \mathrm{H} \longrightarrow_{30}^{65} \mathrm{Zn}+\gamma\)

Some important discoveries in scientific history that contributed to the development of nuclear chemistry are listed below. Briefly, describe each discovery, identify prominent scientists who contributed to it, and comment on the significance of the discovery to the development of this field. (a) \(1896,\) the discovery of radioactivity (b) \(1898,\) the identification of radium and polonium (c) \(1919,\) the first artificial nuclear reaction

Boron is an effective absorber of neutrons. When boron-10 is bombarded by neutrons, an \(\alpha\) particle is emitted. Write an equation for this nuclear reaction.

Some of the reactions explored by Ernest Rutherford (pages 67 and 1166 ) and others are listed below. Identify the unknown species in each reaction. (a) \(^{14} \mathrm{N}+_{2}^{4} \mathrm{He} \longrightarrow^{17}_{8} \mathrm{O}+?\) (b) \(^{9}_{4} \mathrm{Be}+_{2}^{4} \mathrm{He} \longrightarrow ?+\\_{1}^{6} \mathrm{n}\) (c) \(?+\\_{4}^{2} \mathrm{He} \longrightarrow_{15}^{30} \mathrm{P}+\\_{1}^{0} \mathrm{n}\) (d) \(^{233} \mathrm{Pu}+_{2}^{4} \mathrm{He} \longrightarrow ?+\\_{1}^{0} \mathrm{n}\)

A technique to date geological samples uses rubidium-87, a long-lived radioactive isotope of rubidium \(\left(t_{1 / 2}=4.8 \times 10^{10} \text { years }\right)\) Rubidium-87 decays by \(\beta\) emission to strontium- \(87 .\) If rubidium-87 is part of a rock or mineral, then strontium-87 will remain trapped within the crystalline structure of the rock. The age of the rock dates back to the time when the rock solidified. Chemical analysis of the rock gives the amounts of \(^{87} \mathrm{Rb}\) and \(^{87} \mathrm{Sr} .\) From these data, the fraction of \(^{87} \mathrm{Rb}\) that remains can be calculated. Suppose analysis of a stony meteorite determined that \(1.8 \mathrm{mmol}\) of \(^{87} \mathrm{Rb}\) and \(1.6 \mathrm{mmol}\) of \(^{87} \mathrm{Sr}\) (the portion of \(^{87} \mathrm{Sr}\) formed by decomposition of \(^{87} \mathrm{Rb}\) ) were present. Estimate the age of the meteorite. (Hint: The amount of \(^{87} \mathrm{Rb}\) at \(t_{0}\) is moles \(^{87} \mathrm{Rb}+\) moles \(^{87} \mathrm{Sr} .\) )

Tritium, \(_{1}^{3} \mathrm{H},\) is one of the nuclei used in fusion reactions. This isotope is radioactive, with a halflife of 12.3 years. Like carbon- \(14,\) tritium is formed in the upper atmosphere from cosmic radiation, and it is found in trace amounts on Earth. To obtain the amounts required for a fusion reaction, however, it must be made via a nuclear reaction. The reaction of \(_{3}^{6}\) Li with a neutron produces tritium and an \(\alpha\) particle. Write an equation for this nuclear reaction.

Phosphorus occurs in nature as a single isotope, phosphorus-31. Neutron irradiation of phosphorus-31 produces phosphorus-32, a \(\beta\) emitter with a half-life of 14.28 days. Assume you have a sample containing phosphorus-32 that has a rate of decay of \(3.2 \times 10^{6} \mathrm{dpm} .\) Draw a graph showing disintegrations per minute as a function of time during a period of 1 year.

In June \(1972,\) natural fission reactors, which operated billions of years ago, were discovered in Oklo, Gabon (page 1178 ). At present, natural uranium contains 0.72\% \(^{235}\) U. How many years ago did natural uranium contain 3.0\% \(^{235} \mathrm{U}\), the amount needed to sustain a natural reactor? \((t_{1 / 2} \text { for }^{235} \mathrm{U}\text { is }7.04 \times 10^{8} \text { years. })\)

Some important discoveries in scientific history that contributed to the development of nuclear chemistry are listed below. Briefly, describe each discovery, identify prominent scientists who contributed to it, and comment on the significance of the discovery to the development of this field. (a) \(1905,\) theory of special relativity (b) \(1932,(\mathrm{n}, \gamma)\) reactions (c) \(1939,\) fission reactions

A piece of charred bone found in the ruins of a Nativee \(e\) American village has a \(^{14} \mathrm{C} /^{12} \mathrm{C}\) ratio that is \(72 \%\) of the ratio found in living organisms. Calculate the age of the bone fragment. $$\left(t_{1/2} \text { for }^{14} \mathrm{C} \text { is } 5.73 \times 10^{3}\text { years.) }\right.$$

A sample of wood from a Thracian chariot found in an excavation in Bulgaria has a \(^{14} \mathrm{C}\) activity of \(11.2 \mathrm{dpm} / \mathrm{g} .\) Estimate the age of the chariot and the year it was made. \(\left(t_{1 / 2} \text { for }^{14} \mathrm{C} \text { is } 5.73 \times 10^{3}\right.\)years, andthe activity of \(^{14} \mathrm{C}\) in living material is \(14.0 \mathrm{dpm} / \mathrm{g} .\) )

Sodium-23 (in a sample of NaCl) is subjected to neutron bombardment in a nuclear reactor to produce \(^{24}\) Na. When removed from the reactor, the sample is radioactive, with \(\beta\) activity of \(2.54 \times 10^{4} \mathrm{dpm} .\) The decrease in radioactivity over time was studied, producing the following data: (TABLE CANNOT COPY) (a) Write equations for the neutron capture reaction and for the reaction in which the product of this reaction decays by \(\beta\) emission. (b) Determine the half-life of sodium- 24