Chapter 18

Two common units of radiation used in newspaper and news magazine articles are the rad and rem. What does each measure? Which would you use in an article describing the damage an atomic bomb would inflict on a human population? What relationship does the gray have with these units?

Which electrical power plant - fossil fuel or nuclearexposes a community to more nuclear radiation? Explain why.

Explain how our own bodies are sources of nuclear radiation.

Describe the main source of radiation exposure during jet plane travel.

Why are foods irradiated with gamma rays instead of alpha or beta particles?

X-rays and PET scans are two medical imaging techniques. How are they similar and how are they different?

To measure the volume of the blood system of an animal, this experiment was done. A 1.0 -mL sample of an aqueous solution containing tritium with an activity of \(2.0 \times 10^{6} \mathrm{~s}^{-1}\) was injected into the bloodstream. After time was allowed for complete circulatory mixing, a 1.0-mL blood sample was withdrawn and found to have an activity of \(1.5 \times 10^{4} \mathrm{~s}^{-1}\). Calculate the volume of the circulatory system. (The half- life of tritium is 12.3 years, so this experiment assumes that only a negligible quantity of tritium has decayed during the experiment.)

Cobalt- 60 is a therapeutic radioisotope used in treating certain cancers. A sample of cobalt-60 initially disintegrates at a rate of \(4.3 \times 10^{6} \mathrm{~s}^{-1}\) and after 21.2 years the rate has dropped to \(2.6 \times 10^{5} \mathrm{~s}^{-1}\). Calculate the half-life of cobalt- 60

Radioactive nitrogen-13 has a half-life of 10. minutes. Calculate the mass of this isotope that remains after an hour in a sample that originally contained \(96 \mathrm{mg}\).

The half-life of molybdenum-99 is 67.0 hours. Calculate how much of a \(1.000-\mathrm{mg}\) sample of \({ }^{99} \mathrm{Mo}\) is left after 335 hours. Determine how many half-lives it underwent.

The oldest known fossil cells were found in South Africa. The fossil has been dated by the reaction $$ { }_{37}^{87} \mathrm{Rb} \longrightarrow{ }_{38}^{87} \mathrm{Sr}+{ }_{-1}^{0} \mathrm{e} \quad t_{1 / 2}=4.9 \times 10^{10} \text { years } $$ If the ratio of the present quantity of \({ }^{87} \mathrm{Rb}\) to the original quantity is \(0.951,\) calculate the age of the fossil cells.

On December \(2,1942,\) the first man-made self-sustaining nuclear fission chain reactor was operated by Enrico Fermi and others under the University of Chicago stadium. In June 1972 , natural fission reactors, which operated billions of years ago, were discovered in Oklo, Gabon. At present, natural uranium contains \(0.72 \%{ }_{92}^{235} \mathrm{U}\). How many years ago did natural uranium contain \(3.0 \%\) \({ }_{92}^{235} \mathrm{U},\) sufficient to sustain a natural reactor? \(\left(t_{1 / 2}\right.\) for \({ }_{92}^{235} \mathrm{U}=\) \(7.04 \times 10^{8}\) years.

Element 117 was synthesized by collision of calcium- 48 nuclei with berkelium-249 nuclei. Two isotopes of element 117 were formed \(-\) one when three neutrons were emitted; the other when four neutrons were emitted for each 117 nucleus formed. (a) Write a balanced nuclear equation to represent the formation of each isotope. (b) The lighter isotope of element 117 undergoes three successive alpha particle emissions. Write a series of balanced nuclear equations to represent this sequence. (c) The heavier isotope of element 117 undergoes six successive alpha particle emissions. Write a series of balanced nuclear equations to represent this sequence. (d) Identify the group of the periodic table to which element 117 belongs. (e) What name is commonly used for that group?

Element 118 was first synthesized by collision of calcium- 48 nuclei with californium-249 nuclei. Three neutrons were emitted for each 118 nucleus formed. (a) Write a balanced nuclear equation to represent this process. (b) The element 118 nucleus underwent three successive alpha particle emissions. Write a series of balanced nuclear equations to represent this sequence. (c) Identify the group of the periodic table to which element 118 belongs. (d) What name is commonly used for that group?

In June 2009 , researchers at the Joint Institute of Nuclear Research in Dubna, Russia, began continuous bombardment of a \(22-\mathrm{mg}\) target of berkelium- 249 atoms with calcium- 48 nuclei in an attempt to synthesize element 117 . The bombardment continued until January 2010 when evidence indicated that a few atoms of the new element had been synthesized. The half- life of berkelium- 249 is 330 days. Assuming that the reaction period was 240 days, calculate the mass of berkelium-249 remaining.

A \(60-\mathrm{kg}\) woman has an average of \(145 \mathrm{~g}\) of potassium in her body. Of this potassium, \(0.0117 \%\) is radioactive potassium-40, which has a half-life of \(1.2 \times 10^{9}\) yr. Calculate the radioactivity (Bq) emitted from the potassium- 40 .

The mass of the Sun is about \(2 \times 10^{30} \mathrm{~kg}\). The Sun is mostly hydrogen and it emits energy at a rate of about \(4 \times 10^{26} \mathrm{~J} / \mathrm{s}\), principally by the fusion of protons into helium-4 nuclei. Calculate how long it would take for the Sun to lose \(50 \%\) of its mass of \({ }^{1} \mathrm{H}\) at this rate.

In Chapter 12 it was stated that chemical equilibrium is dynamic. Consider this equilibrium \(\mathrm{CH}_{3} \mathrm{COOH}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{CH}_{3} \mathrm{COO}^{-}(\mathrm{aq})+\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})\) Choose a radioisotope that could be used as a tracer to demonstrate that this equilibrium is dynamic. Explain how an experiment using the tracer could show the equilibrium is dynamic.

When a wine was analyzed for its tritium, \({ }_{1}^{3} \mathrm{H},\) content, it was found to contain \(1.45 \%\) of the tritium originally present when the wine was produced. Determine the age of the wine. \(\left(t_{1 / 2}\right.\) of \({ }_{1}^{3} \mathrm{H}=12.3\) years. \()\)

Radioactive isotopes are often used as "tracers" to follow an atom through a chemical reaction. Acetic acid reacts with methanol, \(\mathrm{CH}_{3} \mathrm{OH}\), by eliminating a molecule of \(\mathrm{H}_{2} \mathrm{O}\) to form methyl acetate, \(\mathrm{CH}_{3} \mathrm{COOCH}_{3}\). Explain how you would use the radioactive isotope \({ }^{18} \mathrm{O}\) to show whether the oxygen atom in the water product comes from the \(-\mathrm{OH}\) of the acid or the \(-\mathrm{OH}\) of the alcohol. $$ \begin{aligned} &\mathrm{CH}_{3} \mathrm{COOH}+\mathrm{CH}_{3} \mathrm{OH} \longrightarrow \mathrm{CH}_{3} \mathrm{COOCH}_{3}+\mathrm{H}_{2} \mathrm{O}\\\ &\begin{array}{lll} \text { acetic acid } & \text { methanol } & \text { methyl acetate } \end{array} \end{aligned} $$

If a radioisotope is used for diagnosis (e.g., detecting cancer), it should decay by gamma radiation. However, if its use is therapeutic (e.g., treating cancer), it should decay by alpha or beta radiation. Explain why in terms of ionizing and penetrating power.

During the Three Mile Island incident, people in central Pennsylvania were concerned that strontium-90 (a beta emitter) released from the reactor could become a health threat (it did not). Where would this isotope collect in the body? If so, what types of problems could it cause?

Classify the isotopes \({ }^{17} \mathrm{Ne},{ }^{20} \mathrm{Ne},\) and \({ }^{23} \mathrm{Ne}\) as stable or unstable. What type of decay would you expect the unstable isotope(s) to have?

This demonstration was carried out to illustrate the concept of a nuclear chain reaction. Explain the connections between the demonstration and the reaction. Eighty mousetraps are arranged side by side in eight rows of ten traps each. Each trap is set with two rubber stoppers for bait. A small plastic mouse is tossed into the middle of the traps, setting off one trap, which in turn sets off two traps and so on until all the traps are sprung.

Most students have no trouble understanding that \(1.5 \mathrm{~g}\) of a \(24-g\) sample of a radioisotope would remain after \(8 \mathrm{~h}\) if it had \(t_{1 / 2}=2 \mathrm{~h}\). What they don't always understand is where the other \(22.5 \mathrm{~g}\) went. How would you explain this disappearance to another student?

Nuclear chemistry is a topic that raises many debatable issues. Briefly discuss your views on the following. (a) Twice a year the general public is allowed to visit the Trinity Site in Alamogordo, New Mexico, where the first atomic bomb was tested. If you had the opportunity to do so, would you visit the site? Explain your answer. (b) Now that the Cold War has ended, should the United States stockpile nuclear weapons? Explain your answer. (c) The practice of sterilizing food by irradiation is controversial in the United States. What are some of the possible advantages and disadvantages of this practice? Explain your answer.

All radioactive decays are first order. Why is this so?

A sample of the alpha emitter \({ }_{86}^{222} \mathrm{Rn}\) had an initial activity, \(A_{0},\) of \(7.00 \times 10^{4}\) Bq. After 10.0 days its activity, \(A\) had fallen to \(1.15 \times 10^{4} \mathrm{~Bq} .\) Calculate the decay constant and half-life of radon-222.

A chemist is setting up an experiment using \({ }_{20}^{47} \mathrm{Ca},\) which has a half-life of 4.5 days. She needs \(10.0 \mu \mathrm{g}\) of the calcium. Calculate the minimum mass ( \(\mu \mathrm{g}\) ) of \({ }_{20}^{47} \mathrm{CaCO}_{3}\), she must order if the delivery time is 50 hours.