Chapter 18

Compare nuclear and chemical reactions in terms of changes in reactants, type of products formed, and conservation of matter and energy.

What is meant by the "peninsula of stability"?

Describe the basis for and define the binding energy of a nucleus.

If the mass number of an isotope is much greater than twice the atomic number, what type of radioactive decay might you expect?

If the number of neutrons in an isotope is much less than the number of protons, what type of radioactive decay might you expect?

Define critical mass and chain reaction.

What is the difference between nuclear fission and nuclear fusion? Illustrate your answer with an example of each.

Use the Internet to locate the nuclear reactor power plant nearest to your campus residence. Do you consider the reactor to pose a threat to your health and safety? If so, why? If not, why not?

Name at least two uses of radioactive isotopes (outside of their use in power reactors and weapons).

By what processes do these transformations occur? (a) Thorium- 230 to radium- 226 (b) Cesium-137 to barium-137 (c) Potassium- 38 to argon- 38 (d) Zirconium-97 to niobium-97

By what processes do these transformations occur? (a) Uranium-238 to thorium-234 (b) Iodine-131 to xenon-131 (c) Nitrogen- 13 to carbon- 13 (d) Bismuth-214 to polonium-214

Write a balanced nuclear equation for each word statement. (a) Magnesium- 28 undergoes \(\beta\) emission. (b) When uranium- 238 is reacted with carbon-12, four neutrons are emitted and a new element forms. (c) Hydrogen- 2 and helium- 3 react to form helium-4 and another particle. (d) Argon- 38 forms by positron emission. (e) Platinum- 175 forms osmium- 171 by spontaneous radioactive decay.

Write a balanced nuclear equation for each word statement. (a) Einsteinium- 253 combines with an alpha particle to form a neutron and a new element. (b) Nitrogen-13 undergoes positron emission. (c) Iridium- 178 captures an electron to form a stable nucleus. (d) A proton and boron-11 fuse, forming three identical particles. (e) Nobelium-252 and six neutrons form when carbon-12 collides with a transuranium isotope.

One radioactive series that begins with uranium-235 and ends with lead-207 undergoes this sequence of emission reactions: \(\alpha, \beta, \alpha, \beta, \alpha, \alpha, \alpha, \alpha, \beta, \beta, \alpha .\) Identify the radioisotope produced in each of the first five steps.

One radioactive series that begins with uranium- 235 and ends with lead-207 undergoes this sequence of emission reactions: \(\alpha, \beta, \alpha, \beta, \alpha, \alpha, \alpha, \alpha, \beta, \beta, \alpha .\) Identify the radioisotope produced in each of the last six steps.

Radon-222 is unstable and its presence in homes may constitute a health hazard. It decays by this sequence of emissions: \(\alpha, \alpha, \beta, \beta, \alpha, \beta, \beta, \alpha .\) Write the sequence of nuclear reactions leading to the final product nucleus, which is stable.

Write a nuclear equation for the type of decay each of these unstable isotopes is most likely to undergo. (a) Neon-19 (b) Thorium- 230 (c) Bromine- 82 (d) Polonium-212

Write a nuclear equation for the type of decay each of these unstable isotopes is most likely to undergo. (a) Silver-114 (b) Sodium-21 (c) Radium-226 (d) Iron-59

Boron has two stable isotopes, \({ }^{10} \mathrm{~B}\) (abundance \(=\) \(19.78 \%\) ) and \({ }^{11} \mathrm{~B}\) (abundance \(=80.22 \%\) ). Calculate the binding energies per nucleon of these two nuclei and compare their stabilities. The required masses (in \(\mathrm{g} / \mathrm{mol}\) ) are \({ }_{1}^{1} \mathrm{H}=1.00783\); \({ }_{0}^{1} \mathrm{n}=1.00867 ;{ }_{5}^{10} \mathrm{~B}=10.01294 ;\) and \({ }_{5}^{11} \mathrm{~B}=11.00931 .\)

Calculate the binding energy in kJ per mole of \(\mathrm{P}\) for the formation of \({ }_{15}^{30} \mathrm{P}\) and \({ }_{15}^{31} \mathrm{P}\) $$ \begin{array}{l} 15{ }_{1}^{1} \mathrm{H}+15{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{15}^{30} \mathrm{P} \\ 15{ }_{1}^{1} \mathrm{H}+16{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{15}^{31} \mathrm{P} \end{array} $$ Which is the more stable isotope? The required masses (in \(\mathrm{g} / \mathrm{mol}\) ) are \({ }_{1}^{1} \mathrm{H}=1.00783 ;{ }_{0}^{1} \mathrm{n}=1.00867 ;{ }_{15}^{30} \mathrm{P}=\) \(29.97832 ;\) and \({ }_{15}^{31} \mathrm{P}=30.97376 .\)

Sodium- 24 is a diagnostic radioisotope used to measure blood circulation time. Calculate the mass (mg) of a \(20-\mathrm{mg}\) sample of sodium- 24 that remains after 1 day and 6 hours if sodium- 24 has \(t_{1 / 2}=15\) hours.

Iron- 59 in the form of iron(II) citrate is used in iron metabolism studies. Its half-life is 44.5 days. If you start with \(0.56 \mathrm{mg}\) iron- 59 , calculate the mass (mg) that remains after 1 year.

Iodine- 131 is used in the form of sodium iodide to treat cancer of the thyroid. (a) The isotope decays by ejecting a \(\beta\) particle. Write a balanced equation to show this process. (b) The isotope has a half-life of 8.04 days. If you begin with \(25.0 \mathrm{mg}\) of radioactive \(\mathrm{Na}^{131} \mathrm{I},\) calculate the mass (mg) that remains after 32.2 days.

Phosphorus- 32 is used in the form of \(\mathrm{Na}_{2} \mathrm{H}^{32} \mathrm{PO}_{4}\) in the treatment of chronic myeloid leukemia. (a) The isotope decays by emitting a \(\beta\) particle. Write a balanced equation to show this process. (b) The half-life of \({ }^{32} \mathrm{P}\) is 14.3 days. If you begin with \(9.6 \mathrm{mg}\) radioactive \(\mathrm{Na}_{2} \mathrm{H}^{32} \mathrm{PO}_{4},\) calculate what mass (mg) remains after 28.6 days.

Calculate the half-life of a radioisotope if it decays to \(12.5 \%\) of its radioactivity in 12 years.

After 2 hours, tantalum- 172 has \(\frac{1}{16}\) of its initial radioactivity. Calculate its half-life (s).

Radioisotopes of iodine are widely used in medicine. For example, iodine-131 \(\left(t_{1 / 2}=8.04\right.\) days) is used to treat thyroid cancer. If you ingest a sample of \(\mathrm{Na}^{131} \mathrm{I},\) calculate the time required for the isotope to decrease to \(5.0 \%\) of its original activity.

The noble gas radon has been the focus of much attention because it may be 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) Calculate the time required for a sample of radon to decrease to \(10.0 \%\) of its original activity.

A sample of wood from a Thracian chariot found in an excavation in Bulgaria has a \({ }^{14} \mathrm{C}\) activity of 11.2 disintegrations per minute per gram. Estimate the age of the chariot and the year it was made. \(\left(t_{1 / 2}\right.\) for \({ }^{14} \mathrm{C}\) is \(5.73 \times 10^{3}\) years, and the activity of \({ }^{14} \mathrm{C}\) in living material is 15.3 disintegrations per minute per gram.)

Calculate the time (s) required for a sample of plutonium-239 with a half-life of \(2.4 \times 10^{4}\) years to decay to \(1 \%\) of its original activity.

A 1.00 -g sample of wood from an archaeological site gave 4100 disintegrations of \({ }^{14} \mathrm{C}\) in a 10 -hour measurement. In the same time, a 1.00 -g modern sample gave 9200 disintegrations. Calculate the age of the wood.

Fluorine-18, a diagnostic radioisotope used to evaluate cardiovascular conditions, is made by reaction of oxygen- 18 with a proton. A neutron is also produced in addition to fluorine-18. Write a balanced nuclear equation to represent this process.

Nitrogen-13, a diagnostic radioisotope used to detect tumors, is made by reaction of oxygen- 16 with a proton. An alpha particle is also produced in addition to nitrogen-13. Write a balanced nuclear equation to represent this process.

In \(2006,\) Alexander Litvinenko, a vocal critic of the Putin government in Russia, was poisoned in London with a lethal dose of polonium- 210 injected by Russian agents. Polonium- 210 is synthesized by the uptake of a neutron by bismuth-209. Write a balanced nuclear equation to represent this process.

In 1998 , researchers in Dubna, Russia, synthesized element 112 , copernicium, by reaction of uranium- 238 nuclei with calcium- 48 nuclei. The copernicium- 283 isotope was produced along with neutrons. Write a balanced nuclear equation to represent this synthesis.

The synthesis of \({ }_{116}^{292} \mathrm{Lv}\) has been attempted by trying to merge calcium- 40 and californium- 249 nuclei, but has not yet succeeded. Write a balanced nuclear equation to represent this attempted synthesis.

There are two isotopes of americium, both with half-lives sufficiently long to allow the handling of large quantities. Americium-241, an alpha emitter, has a half-life of 433 years; it is used in gauging the thickness of materials and in smoke detectors. This 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.

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

To synthesize the heavier transuranium elements, one must react a lighter nucleus with a relatively large particle. If you know that the products of such a reaction are californium- 246 and four neutrons, what particle must have reacted with uranium- 238 atoms?

The officially named element with the highest atomic number is livermorium, \({ }_{116}^{293} \mathrm{Lv}\), named to honor the long history of the synthesis of post-uranium elements at the Lawrence Livermore National Laboratory in Berkeley, CA. In attempts to make elements with a higher atomic number than \(116,\) reactions have been attempted between californium- 249 and calcium-48. Determine the atomic number of the element that would be formed.

Elements are formed by nuclear fusion reactions. One step in this process is so-called "helium burning", the fusion of two helium- 4 nuclei to produce beryllium- 8 . Write a balanced nuclear equation to represent this process.

Elements are formed by nuclear fusion reactions including so-called "carbon burning", the fusion of two carbon-12 nuclei to produce sodium- 23 and a proton. Write a balanced nuclear equation to represent this process.

Elements are formed by nuclear fusion reactions such as so-called "carbon and oxygen burning", the fusion of a carbon-12 nucleus with an oxygen- 16 nucleus to produce silicon-28. Write a balanced nuclear equation to represent this process.

Under proper conditions, fusion of a helium- 3 nucleus with a proton produces helium-4 plus a neutron. Write a balanced nuclear equation to represent this process.

Name the fundamental parts of a nuclear fission reactor and describe their functions.

Explain why it is easier for a nucleus to capture a neutron than for a nucleus to capture a proton.

Explain why no commercial fusion reactors are in operation today.

A concern in the nuclear power industry is that, if nuclear power becomes more widely used, there may be serious shortages in worldwide supplies of fissionable uranium. One solution is to build breeder reactors that manufacture more fuel than they consume. One such cycle works as follows: (i) \(\mathrm{A}^{238} \mathrm{U}\) nucleus collides with a neutron to produce \({ }^{239} \mathrm{U}\). (ii) \({ }^{239} \mathrm{U}\) decays by \(\beta\) emission \(\left(t_{1 / 2}=24\right.\) minutes \()\) to give an isotope of neptunium. (iii) The neptunium isotope decays by \(\beta\) emission to give a plutonium isotope. (iv) The plutonium isotope is fissionable. On its collision with a neutron, fission occurs and gives energy, at least two neutrons, and other nuclei as products. Write an equation for each of these steps, and explain how this process can be used to breed more fuel than the reactor originally contained and still produce energy.

In 2012, a radiation reading of 73 sieverts (Sv) was recorded in the containment structure at the Fukushima Daiichi reactor 2 . Assuming a quality factor of 20 . convert this reading to: (a) rads. (b) grays (Gy). (c) mrem.

The average annual dose of ionizing radiation in the United States is 360 mrem. Convert this value to (a) sieverts (Sv). (b) rads (assume a quality factor of \(10 .)\). (c) grays (Gy).