Chapter 21

What are some of the molecular effects of exposure to radioactivity?

Describe the dangers of exposure to radon-222.

Periodic outbreaks of food poisoning from E. coli-contaminated meat have renewed the debate about irradiation as an effective treatment of food. In one newspaper article on the subject, the following statement appeared: "Irradiating food destroys bacteria by breaking apart their molecular structure." How would you improve or expand on this explanation?

Dental X-rays expose patients to about \(5 \mu\) Sv of radiation. Given an RBE of 1 for \(\mathrm{X}\) -rays, how many grays of radiation does \(5 \mu \mathrm{Sv}\) represent? For a 50 kg person, how much energy does \(5 \mu\) Sv correspond to?

Strontium-90 in Milk In the years immediately following the explosion at the Chernobyl nuclear power plant, the concentration of \({ }^{90} \mathrm{Sr}\) in cow's milk in southern Europe was slightly elevated. Some samples contained as much as \(1.25 \mathrm{~Bq} / \mathrm{L}\) of \({ }^{90} \mathrm{Sr}\) radioactivity. The half-life of strontium-90 is 28.8 years. a. Write a balanced nuclear equation describing the decay of \({ }^{90} \mathrm{Sr}\). b. How many atoms of \({ }^{90} \mathrm{Sr}\) are in a \(200 \mathrm{~mL}\) glass of milk with \(1.25 \mathrm{~Bq} / \mathrm{L}\) of \({ }^{90} \mathrm{Sr}\) radioactivity? c. Why would strontium-90 be more concentrated in milk than other foods, such as grains, fruits, or vegetables?

If exactly \(1.00 \mu \mathrm{g}\) of \(^{226} \mathrm{Ra}\) was applied to the glow-in-the-dark dial of a wristwatch made in \(1914,\) how radioactive is the watch today? Express your answer in microcuries and becquerels. The half-life of \(226 \mathrm{Ra}\) is \(1.60 \times 10^{3}\) years.

In \(1999,\) the U.S. Environmental Protection Agency set a maximum radon level for drinking water at \(4.0 \mathrm{pCi}\) per milliliter. a. How many decay events occur per second in a milliliter of water for this level of radon radioactivity? b. If the above radioactivity were due to the decay of \(^{222} \operatorname{Rn}\left(t_{1 / 2}=3.8 \text { days }\right),\) how many \(^{222} \mathrm{Rn}\) atoms would there be in \(1.0 \mathrm{mL}\) of water?

A former Russian spy died from radiation sickness in 2006 after dining at a London restaurant where he apparently ingested polonium-210. The other people at his table did not suffer from radiation sickness, even though they were very near the radioactive food the victim ate. Why were they not affected?

How does the selection of an isotope for radiotherapy relate to (a) its half- life, (b) its mode of decay, and (c) the properties of the products of decay?

Are the same radioactive isotopes likely to be used for both imaging and cancer treatment? Why or why not?

Predict the most likely mode of decay for the following isotopes used as imaging agents in nuclear medicine: (a) \(^{197} \mathrm{Hg}\) (kidney); (b) \(^{75} \mathrm{Se}\) (parathyroid gland); (c) \(^{18} \mathrm{F}\) (bone).

Predict the most likely mode of decay for the following isotopes used as imaging agents in nuclear medicine: (a) \(^{133} \mathrm{Xe}\) (cerebral blood flow); (b) \(^{57}\) Co (tumor detection) (c) \(^{51} \mathrm{Cr}\) (red blood cell mass); (d) \(^{67} \mathrm{Ga}\) (tumor detection).

A 1.00 mg sample of \(^{192}\) Ir was inserted into the artery of a heart patient. After 30 days, 0.756 mg remained. What is the half-life of \(^{192} \mathrm{Ir} ?\)

A patient is administered mercury-197 to evaluate kidney function. Mercury- 197 has a half-life of 65 hours. What fraction of an initial dose of mercury-197 remains after 6 days?

Rhodium-105 is an isotope currently under investigation in diagnostic applications. The half-life of \(^{105} \mathrm{Rh}\) is \(35.4 \mathrm{h}\) which is sufficiently long for transport from the supplier a hospital. A supplier ships \(250 \mathrm{mg}\) of \(^{105} \mathrm{RhCl}_{3}\) overnight (12 hours). a. What percentage of the \(^{105}\) Rh remains upon arrival? b. How long will it take for \(95 \%\) of the \(^{105} \mathrm{Rh}\) to decay?

Cancer Palladium-103 is used to treat prostate cancer by inserting a small \((1 \mathrm{mm} \times 5 \mathrm{mm})\) cylindrical piece of \(^{103} \mathrm{Pd}\) directly into the tumor. How long will it take for \(85 \%\) of the \(^{103} \mathrm{Pd}\) to decay, given that \(t_{1 / 2}=17\) days?

In boron neutron-capture therapy (BNCT), a patient is given a compound containing \(^{10} \mathrm{B}\) that accumulates inside cancer tumors. Then the tumors are irradiated with neutrons, which are absorbed by \(^{10} \mathrm{B}\) nuclei. The product of neutron capture is an unstable form of \(^{11} \mathrm{B}\) that undergoes \(\alpha\) decay to \(^{7} \mathrm{Li}\). a. Write a balanced nuclear equation for the neutron absorption and \(\alpha\) decay process. b. Calculate the energy released by each nucleus of boron- 10 that captures a neutron and undergoes \(\alpha\) decay, given the following masses of the particles in the process: \(^{10} \mathrm{B}\left(10.0129 \text { amu) },^{7} \mathrm{Li}(7.01600\text { amu) }\right.\) \(^{4} \mathrm{He}(4.00260 \mathrm{amu}),\) and \(^{1} \mathrm{n}(1.00866 \mathrm{amu})\) c. Why is the formation of a nuclide that undergoes \(\alpha\) decay a particularly effective cancer therapy?

Thirty years before the creation of anti-hydrogen, television producer Gene Roddenberry \((1921-1991)\) proposed to use this form of antimatter to fuel the powerful "warp" engines of the fictional star ship Enterprise. a. Why would anti-hydrogen have been a particularly suitable fuel? b. Describe the challenges of storing such a fuel on a star ship.

Tiny concentrations of radioactive tritium \(_{1}^{3} \mathrm{H}\),occur naturally in rain and groundwater. The half-life of \(_{1}^{3} \mathrm{H}\) is 12 years. Assuming that tiny concentrations of tritium can be determined accurately, could the isotope be used to determine whether a bottle of wine with the year 1969 on its label actually contained wine made from grapes that were grown in \(1969 ?\) Explain your answer.

In Section 21.6 we state that "no energy would be released if two \(^{4} \mathrm{He}\) nuclei were to fuse together to form \(^{8} \mathrm{Be}\). Similarly, \(^{8} \mathrm{Be}\) nuclei require no energy to spontaneously decompose into \(^{4}\) He nuclei, so they would immediately do so." Verify this statement by calculating the binding energy of \(^{8} \mathrm{Be}\) and comparing it to that of \(^{4} \mathrm{He}\).

How much energy is required to remove a neutron from the nucleus of an atom of carbon- 13 (mass \(=13.00335\) amu)? (Hint: The mass of an atom of carbon-12 is exactly \(12.00000 \text { amu. })\)

Americium \(-241\left(t_{1 / 2}=433 \mathrm{yr}\right)\),is used in smoke detectors. The \(\alpha\) particles from this isotope ionize nitrogen and oxygen in the air, creating an electric current. When smoke is present, the current decreases, setting off the alarm. a. Does a smoke detector bear a closer resemblance to a Geiger counter or to a scintillation counter? b. How long will it take for the radioactivity of a sample of \(^{241} \mathrm{Am}\) to drop to \(1 \%\) of its original radioactivity? c. Why are smoke detectors containing \(^{241} \mathrm{Am}\) safe to handle without protective equipment?

Potassium- 40 is a radioactive isotope of potassium, a very common element in terrestrial rocks, which decays to \(^{40}\) Ar with a half-life of \(1.28 \times 10^{9}\) years. By measuring the ratio of \(^{40} \mathrm{Ar}\) to \(^{40} \mathrm{K},\) geologists can to determine the age of ancient rocks. a. Balance the nuclear equations for the decay of \(^{40} \mathrm{K}\) by identifying the missing isotope or particle.$$\begin{array}{l}^{40} \mathrm{K} \rightarrow^{40} \mathrm{Ar}+? \\\^{40} \mathrm{K} \rightarrow +_{-1}^{0} \beta\end{array}$$.b. Why might \(^{40} \mathrm{K}\) decay by two different pathways? c. Only about \(11 \%\) of the \(^{40} \mathrm{K}\) decays to \(^{40} \mathrm{Ar}\). If the ratio of \(^{40} \mathrm{Ar}\) to \(^{40} \mathrm{K}\) in a rock is found to be \(0.435,\) how old is the rock? d. Why don't geologists measure the \(^{40} \mathrm{Ca}:^{40} \mathrm{K}\) ratio instead?

In 2006 an international team of scientists confirmed the synthesis of a total of three atoms of Og (oganesson) in experiments run in 2002 and 2005. They bombarded a \(^{249}\) Cf target with \(^{48}\) Ca nuclei. a. Write a balanced nuclear equation describing the synthesis of \(_{118}^{294} \mathrm{Og}\) b. The synthesized isotope of Og undergoes \(\alpha\) decay \(\left(t_{1 / 2}=0.9 \mathrm{ms}\right) .\) What nuclide is produced by the decay process? c. The nuclide produced in part b also undergoes \(\alpha\) decay \(\left(t_{1 / 2}=10 \mathrm{ms}\right) .\) What nuclide is produced by this decay process? d. The nuclide produced in part c also undergoes \(\alpha\) decay \(\left(t_{1 / 2}=0.16 \mathrm{s}\right) .\) What nuclide is produced by this decay process? e. If you had to select an element that occurs in nature and that has physical and chemical properties similar to Og, which element would it be?

Radiation exposure leads to the ionization of water to \(\mathrm{H}_{2} \mathrm{O}^{+},\) which reacts to form \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{OH}\). Draw Lewis structures for these three molecules or molecular ions.

Dating Cave Paintings Cave paintings in Gua Saleh Cave in Borneo have been dated by measuring the amount of \(^{14} \mathrm{C}\) in calcium carbonate deposits that formed over the pigments used in the paint. The source of the carbonate ion was atmospheric \(\mathrm{CO}_{2}\).a. What is the ratio of the \(^{14} \mathrm{C}\) radioactivity in calcium carbonate that formed 9900 years ago to that in calcium carbonate formed today? b. The archaeologists also used a second method, uranium-thorium dating, to confirm the age of the paintings by measuring trace quantities of these elements present as contaminants in the calcium carbonate. Shown below are two candidates for the U-Th dating method. Which isotope of uranium do you suppose was chosen? Explain your answer. $$\begin{aligned} &t_{1 / 2}=^{233} \mathrm{U} \quad 7.04 \times 10^{8} \mathrm{yr} \quad^{231} \mathrm{Th} \quad \rightarrow \quad^{231} \mathrm{p}_{2} \quad 3 \quad \rightarrow \quad\\\ &t_{1 / 2}=^{234} \mathrm{U} \quad \begin{array}{rl}\rightarrow & ^{230} \mathrm{Th} \\ 2.44 \times 10^{5} \mathrm{yr} & 7.7 \times 10^{4} \mathrm{hr}\end{array} \quad \begin{array}{rl} 226 \mathrm{p}_{2} & \rightarrow \\\1600 & \mathrm{yr}\end{array}\end{aligned}$$

The synthesis of new elements and specific isotopes of known elements in linear accelerators involves the fusion of smaller nuclei. a. An isotope of platinum can be prepared from nickel-64 and tin-124. Write a balanced equation for this nuclear reaction. (You may assume that no neutrons are ejected in the fusion reaction.) b. Substitution of tin- 132 for tin- 124 increases the rate of the fusion reaction 10 times. Which isotope of \(\mathrm{Pt}\) is formed in this reaction?

The first attempt at radiocarbon dating six skeletons discovered in an Italian cave at the beginning of the 20 th century indicated an age of 15,000 years. Redetermination of the age in 2004 indicated an older age for two bones of between 23,300 and 26,400 years. What is the ratio of \(^{14} \mathrm{C}\) in a sample 15,000 years old to one 25,000 years old?

There was once a plan to store radioactive waste that contained plutonium- 239 in the reefs of the Marshall Islands. The planners claimed that the plutonium would be "reasonably safe" after 240,000 years. If the half-life is 24,400 years, what percentage of the \(^{239}\) Pu would remain after 240,000 years?

In 1997 anthropologists uncovered three partial skulls of prehistoric humans in the Ethiopian village of Herto. Based on the amount of \(^{40} \mathrm{Ar}\) in the volcanic ash in which the remains were buried, their age was estimated at between 154,000 and 160,000 years old. a. \(^{40} \mathrm{Ar}\) is produced by the decay of \(^{40} \mathrm{K}\left(t_{1 / 2}=1.28 \times\right.\) \(10^{9}\) yr). Propose a decay mechanism for \(^{40} \mathrm{K}\) to \(^{40} \mathrm{Ar}\). b. Why did the researchers choose \(^{40}\) Ar rather than \(^{14} \mathrm{C}\) as the isotope for dating these remains?

Thorium-232 slowly decays to bismuth-212 \(\left(t_{1 / 2}=1.4 \times 10^{10} \mathrm{yr}\right) .\) Bismuth-212 decays to lead-208 by two pathways: first \(\beta\) and then \(\alpha\) decay, or \(\alpha\) and then \beta decay. The intermediate nuclide in the second pathway is thallium-208. The thallium-208 can be separated from a sample of thorium nitrate by passing a solution of the sample through a filter pad containing ammonium phosphomolybdate. The radioactivity of \(^{208}\) T1 trapped on the filter is measured as a function of time. In one such experiment, the following data were collected: $$\begin{array}{cc}\text { Time (s) } & \text { Counts/min } \\\\\hline 60 & 62 \\\\\hline 120 & 40 \\\\\hline 180 & 35 \\\\\hline 240 & 22 \\\\\hline 300 & 16 \\\\\hline 360 & 10 \\\\\hline\end{array}$$ Use the data in the table to determine the half-life of \(^{208} \mathrm{T} 1 .\)

The following nuclear equations are based on successful attempts to synthesize supermassive elements. Complete each equation by writing the symbol of the supermassive nuclide that was synthesized. a. \({ }_{26}^{58} \mathrm{Fe}+{ }_{83}^{209} \mathrm{Bi} \rightarrow ?+{ }_{0}^{1} \mathrm{n}\) b. \({ }_{28}^{64} \mathrm{Ni}+{ }_{83}^{209} \mathrm{Bi} \rightarrow ?+{ }_{0}^{1} \mathrm{n}\) c. \({ }_{28}^{62} \mathrm{Ni}+{ }_{83}^{208} \mathrm{Pb} \rightarrow ?+{ }_{0}^{1} \mathrm{n}\) d. \({ }_{10}^{22} \mathrm{Ne}+{ }_{97}^{249} \mathrm{Bk} \rightarrow ?+4{ }_{0}^{1} \mathrm{n}\) e. \({ }_{26}^{58} \mathrm{Fe}+{ }_{82}^{208} \mathrm{Pb} \rightarrow ?+{ }_{0}^{1} \mathrm{n}\)

The absorption of a neutron by \(^{11} \mathrm{B}\) produces a radioactive nuclide that decays by either \(\alpha\) decay or \(\beta\) decay. Write balanced nuclear equations describing the decay reactions.

An atom of darmstadtium- 269 was synthesized in 2003 by the bombardment of a \(^{208} \mathrm{Pb}\) target with \(^{62} \mathrm{Ni}\) nuclei. Write a balanced nuclear equation describing the synthesis of \(269 \mathrm{Ds}\).

Isotopes in Geochemistry The relative abundances of the stable isotopes of the elements are not entirely constant. For example, in some geological samples (soils and rocks), the ratio of \(^{87} \mathrm{Sr}\) to \(^{86} \mathrm{Sr}\) is affected by the presence of a radioactive isotope of another element, which slowly undergoes \(\beta\) decay to produce more \(^{87} \mathrm{Sr}\). What is this other isotope?

Rhodium-105 is made by neutron bombardment of \(^{104} \mathrm{Ru}\), which decays to \(^{105} \mathrm{Rh}\) with a half-life of \(4.4 \mathrm{h}\). a. Write a balanced nuclear equation for the formation of \(^{105} \mathrm{Rh}\). b. Calculate how long it will take for 9996 of the \(^{105} \mathrm{Rh}\) to decay.