Chapter 23

Some important discoveries in scientific history that contributed to the development of nuclear chemistry are listed below. Brichy, describe each discovery, identify prominent scientists who contributed to it, and comment on the significance of the discovery to the development of this ficld. (a) \(1896,\) the discovery of radioactivity (b) \(1898,\) the identification of radium and polonium (c) \(1919,\) the first artificial nuclear reaction (d) \(1932,(n, \gamma)\) reactions (e) \(1939,\) fission reactions

In Chapter \(3,\) the law of conservation of mass was introduced as an important principle in chemistry. The discovery of nuclear reactions forced scientists to modify this law. Explain why, and give an example illustrating that mass is not conserved in a nuclear reaction.

Outline how nuclear reactions are carried out in the laboratory. Describe the artificial nuclear reactions used to make an element with an atomic number greater than 92.

Explain how carbon-14 is used to estimate the ages of archeological artifacts. What are the limitations for use of this technique?

Describe how the concept of half-life for nuclear decay is used.

What is a radioactive decay series? Explain why radium and polonium are found in uranium ores.

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 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) bromine-80 (c) cobalt-61 (b) californium-240 (d) carbon-11

(a) Which of the following nuclei decay by \(-1 \beta\) decay? $$^{1} \mathbf{H} \quad^{23} \mathrm{Mg} \quad^{\quad \quad * P} \quad \text { an } \mathrm{Ne}$$ (b) Which of the following nuclei decay by \(+\\{\beta\) decay? \(^{205} \mathrm{U} \quad^{55} \mathrm{CA} \quad^{52} \mathrm{K} \quad^{24} \mathrm{Na}\)

Calculate the binding energy per mole of nucleons for calcium-40, and compare your result with the value in Figure \(23.4 .\) Masses needed for this calculation are (in \(\mathrm{g} / \mathrm{mol}\) ) \(\mathrm{iH}=1.00783, \frac{1}{0} \mathrm{n}=1.00867,\) and \(\underset{20}{a} \mathrm{Ca}=39.96259\).

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 \(^{\text {tses }}\) Au is 2.69 days. If you begin with \(2.8 \mu g\) 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 \(1^{31} \mathrm{I}\), 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 \(^{32} P\) is 14.3 days. If you begin with 4.8 \(\mu g\) of radioactive \(^{32} \mathrm{P}\) in the form of \(\mathrm{Na}_{2} \mathrm{HPO}_{4},\) what mass remains after 28.6 days (about one month)?

Gallium-67 \(\left(t_{44}=78.25\) hours) is used in the medical \right. 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 $$-131\left(t_{4}=8.04 \text { days }\right)$$ 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 \(^{131} 1,\) 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 \(^{22} \mathrm{Rn}\) to \(\mathrm{de}\) crease 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 "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 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 cobali-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. It is used in smoke detectors. The isotope is formed from \(^{2 * 9} \mathrm{Pu}\) by absorption of two neut trons followed by emission of a \(\beta\) particle. Write a balanced equation for this process.

The super-heavy element \(^{2 \times 7}\) Uuq (element 114 ) was made by firing a beam of "Ca ions at \(^{242} \mathrm{Pu}\). Three neutrons were ejected in the reaction. Write a balanced nuclear equation for the synthesis of \(^{2 \pi}\) Uuq.

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?

Element \(\frac{297}{114}\) Uuq decays by \(\alpha\) emission with a half-life of about 5 seconds. Write an equation for this process.

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.

A technique to date geological samples uses rubidium-87, a long-lived radioactive isotope of rubidium $$\left(t_{1}=4.8 \times 10^{10} \text { years }\right)$$. 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 anal. ysis of the rock gives the amounts of \(^{\pi \pi} \mathrm{Rb}\) and \(^{\mathrm{X} 7} \mathrm{Sr}\). From these data, the fraction of \(^{\mathrm{s} 7} \mathrm{Rb}\) that remains can be calculated. Suppose analysis of a stony meteorite determined that 1.8 mmol of \(^{\text {* }}\) Rb and 1.6 mmol of \(^{\text {mige }}\) Sr (the portion of "Sr formed by decomposition of "Rb) were present. Estimate the age of the meteorite. (Hint: The amount of \(^{\mathrm{s} 2} \mathrm{Rb}\) at \(t_{0}\) is moles \(^{\mathrm{s} 7} \mathrm{Rb}+\) moles \(^{\mathrm{s} 7} \mathrm{Sr}\).)

Tritium, \(\frac{3}{1} \mathbf{H},\) is one of the nuclei used in fusion reactions. This isotope is radioactive, with a half-life 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 \(1\) i 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 \(\$ .2 \times 10^{6}\) dpm. Draw a graph showing disintegrations per minute as a function of time during a period of 1 year.

The isotope of polonium that was most likely isolated by Marie Curie in her pioneering studies is polonium-210. A sample of this element was prepared in a nuclear reaction. Initially, its activity ( \(\alpha\) emission) was \(7840 \mathrm{dpm}\). Measuring radioactivity over time produced the data below. Determine the half-life of polonium-210. $$\begin{array}{cc}\text { Activity (dpm) } & \text { Time (days) } \\\\\hline 7840 & 0 \\\7570 & 7 \\\7300 & 14 \\ 5920 & 56 \\\5470 & 72 \\\\\hline\end{array}$$

The oldest-known fossil found in South Africa has been dated based on the decay of Rb-87. $$^{s q} \mathbf{R b} \longrightarrow^{* \tau} \mathbf{S}_{\mathbf{r}}+\underset{-1}{\mathbf{\beta}}^{\mathbf{o}} \boldsymbol{\beta} \quad t_{1 / 2}=4.8 \times 10^{10} \text { years }$$ If the ratio of the present quantity of \(^{\mathrm{A} 7} \mathrm{Rb}\) to the original quantity is \(0.951,\) calculate the age of the fossil.

The principle underlying the isotope dilution method of analysis can be applied to many kinds of problems. Suppose that you, a marine biologist, want to estimate the number of fish in a lake. You release 1000 tagged fish, and after allowing an adequate amount of time for the fish to disperse evenly in the lake, you catch 5250 fish and find that 27 of them have tags. How many fish are in the lake?

Radioactive isotopes are often used as "tracers" to follow an atom through a chemical reaction. The following is an example of this process: Acetic acid reacts with methanol, \(\mathrm{CH}_{5} \mathrm{OH}\), by eliminating a molecule of \(\mathrm{H}_{2} \mathrm{O}\) to form methy acetate, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{CH}_{3}\). Explain how you would use the radioactive isotope \(^{15} \mathbf{O}\) to show whether the oxygen atom in the water product comes from the - OH of the acid or the - OH of the alcohol.

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