Chapter 19

What do the terms mass defect and binding energy mean?

Why is energy released in a nuclear fusion process when the product is an element preceding iron in the periodic table?

What is the binding energy of \(^{6} \mathrm{Li}\), which has a nuclear mass of \(9.98561 \times 10^{-27} \mathrm{kg} ?\)

Our Sun is a fairly small star that has barely enough mass to fuse hydrogen to helium. Calculate the binding energy per nucleon of helium-4 on the basis of these masses: \(\stackrel{4}{2} \mathrm{He}\) $$\left(4.00260 \text { amu), }_{1}^{1} \mathrm{p}(1.00728 \text { amu }), \text { and }_{0}^{1} \mathrm{n}(1.00866 \mathrm{amu})\right.$$

What is the binding energy per nucleon of \(^{12} \mathrm{C},\) the atomic mass of which is 12.00000 amu? (Note: Atomic mass includes the mass of 6 electrons.)

How can the belt of stability be used to predict the probable decay mode of an unstable nuclide?

Compare positron-emission and electron-capture processes.

The ratio of neutrons to protons in stable nuclei increases with increasing atomic number. Use this trend to explain why multiple \(\alpha\) decay steps in the \(^{238} \mathrm{U}\) decay series are often followed by \(\beta\) decay.

Copper- 64 is an unusual radionuclide in that it may undergo \(\beta\) decay, positron emission, or electron capture. What are the products of these decay processes?

Iodine- 137 decays to give xenon- 137 , which decays to give cesium-137. What are the modes of decay in these two reactions?

Write a balanced nuclear equation describing (a) \(\alpha\) decay of curium-242; (b) \(\beta\) decay of magnesium- 28 (c) positron emission by xenon-118; (d) electron capture by cadmium-104.

If the mass number of an isotope is more than twice the atomic number, is the neutron-to-proton ratio less than, greater than, or equal to \(1 ?\)

In each of the following pairs of isotopes, select the isotope that has more protons and the isotope that has more neutrons. Also indicate which pairs of isotopes have the same number of neutrons or protons. (a) \(^{63} \mathrm{Cu}\) and \(^{65} \mathrm{Cu}\) (b) \(^{71}\) Ga and \(^{71} \mathrm{Ge} ;\) (c) \(^{39} \mathrm{K}\) and \(^{40} \mathrm{Ar}\)

Identify the type of radiation emitted or consumed in the following processes: $$\text { a. } \quad \frac{222}{86} \mathrm{Rn} \rightarrow \frac{218}{84} \mathrm{Po}+?$$ $$\text { b. } ^{131}_{53} \mathrm{I} \rightarrow_{54}^{131} \mathrm{Xe}+?$$ $$\text { c. }^{11}_{6} C \rightarrow_{5}^{11} B+?$$ $$\text { d. }^{7}_4{\mathrm{B}} \mathrm{e}+? \rightarrow_{3}^{7} \mathrm{Li}$$

Write a balanced nuclear equation describing the \(\beta\) decay of cesium-137, which is produced in nuclear power plants.

Predict the \(\operatorname{mode}(\mathrm{s})\) of decay for the following radioactive isotopes: \((\mathrm{a})^{10} \mathrm{C} ;\) (b) \(^{19} \mathrm{Ne} ;\) (c) \(^{50} \mathrm{Ti}\)

Predict the mode(s) of decay of the following radionuclides: (a) \(^{24} \mathrm{Ne} ;\) (b) \(^{38} \mathrm{K} ;(\mathrm{c})^{45} \mathrm{Ti} ;(\mathrm{d})^{237} \mathrm{Np}\)

There are isotopes of nitrogen that have as few as 5 or as many as 11 neutrons in each of their nuclei. Write a balanced nuclear equation describing the decay of the isotope with 11 neutrons.

Chlorine has isotopes with mass numbers from 32 through \(39 .\) Two of them, \(^{35} \mathrm{Cl}\) and \(^{37} \mathrm{Cl}\), are stable. a. Which three of the other isotopes emit positrons? b. Which of the other isotopes emit \(\beta\) particles? c. Which one of the other isotopes can emit either positrons or \(\beta\) particles?

Bromine has isotopes with mass numbers from 74 through 90\. Two of them, \(^{79} \mathrm{Br}\) and \(^{81} \mathrm{Br}\), are stable. a. How many of the others emit positrons or undergo electron capture? b. How many of the others emit \(\beta\) particles? c. Which one of the other isotopes can emit either positrons or \(\beta\) particles?

What percentage of a sample's original radioactivity remains after two half- lives?

Explain why rates of nuclear decay are independent of temperature.

The half-life of radon-222, a radioactive gas found in some basements, is 3.82 days. Calculate the decay rate constant of radon- 222

The decay rate constant of sodium- \(24,\) a tracer used in blood studies, is \(4.6 \times 10^{-2} \mathrm{h}^{-1} .\) What is the value of its half-life?

Explosions at a disabled nuclear power station in Fukushima, Japan, in 2011 may have released more cesium- \(137(t_{1 / 2}=30.2\) years) into the ocean than any.other single event. How long will it take the radioactivity of this radionuclide to decay to \(5.0 \%\) of the level released in \(2011 ?\)

Spent fuel removed from nuclear power stations contains plutonium- \(239(t_{1 / 2}=2.41 \times 10^{4}\) years). How long will. it take a sample of this radionuclide to reach a level of radioactivity that is \(2.5 \%\) of the level it had when it was removed from a reactor?

Explain why radiocarbon dating is reliable only for artifacts and fossils younger than about 50,000 years.

Which of the following statements about \(^{14} \mathrm{C}\) dating are true? a. The amount of \(^{14} \mathrm{C}\) in a1l objects is the same. b. Carbon- 14 is unstable and is readily lost from the atmosphere. c. The ratio of \(^{14} \mathrm{C}\) to \(^{12} \mathrm{C}\) in the atmosphere is a constant. d. Living tissue will absorb \(^{12} \mathrm{C}\) but not \(^{14} \mathrm{C}\)

Why is \(^{40} \mathrm{K}\) dating \((t_{1 / 2}=1.28 \times 10^{9}\) years) useful only for rocks older than 300,000 years?

Where does the \(^{14} \mathrm{C}\) found in plants come from?

Geologists who study volcanoes can develop historical profiles of previous eruptions by determining the \(^{14} \mathrm{C} /^{12} \mathrm{C}\) ratios of charred plant remains entrapped in old magma and ash flows. If the uncertainty in determining these ratios is \(0.1 \%,\) could radiocarbon dating distinguish between debris from the eruptions of Mt. Vesuvius that occurred in the years 472 and \(512 ?\) (Hint: Calculate the \(^{14} \mathrm{C} /^{12} \mathrm{C}\) ratios for samples from the two dates.)

What is the difference between a level of radioactivity and a dose of radioactivity?

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 \(\mathrm{RBE}\) 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?

Some workers responding to the explosion at the Chernobyl nuclear power plant were exposed to 5 Sv of radiation, killing many of them. If the exposure was primarily in the form of \(\gamma\) rays with an energy of \(3.3 \times 10^{-14} \mathrm{J}\) and an \(\mathrm{RBE}\) of \(1,\) how many \(\gamma\) rays did an \(80-\) kg person absorb?

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 Bq/L of \(^{90}\) 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 -mL glass of milk with \(1.25 \mathrm{Bq} / \mathrm{L}\) of \(^{90}\) 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 used to paint 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 decay of \(^{222} \mathrm{Rn}\) \(\left(t_{1 / 2}=3.8 \text { days }\right),\) 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 tea the victim drank. 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) \(^{57} \mathrm{Co}\) (tumor detection) (c) \(^{51}\) Cr (red blood cell mass); (d) \(^{67}\) 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 \(^{192}\) Ir?

In a treatment that decreases pain and reduces inflammation of the lining of the knee joint, a sample of dysprosium-165 with a radioactivity of 1100 counts per second was injected into the knee of a patient suffering from rheumatoid arthritis. After \(24 \mathrm{h}\), the radioactivity had dropped to 1.14 counts per second. Calculate the half-life of \(^{165} \mathrm{Dy}\)

A patient is administered mercury-197 to evaluate kidney function. Mercury- 197 has a half-life of \(65 \mathrm{h}\). What fraction of an initial dose of mercury-197 remains after 6 days?

Carbon-11 is an isotope used in positron emission tomography and has a half- life of 20.4 min. How long will it take for \(99 \%\) of the \(^{11} \mathrm{C}\) injected into a patient to decay?

Sodium-24 is used to treat leukemia and has a half-life of 15 h. In a patient injected with a salt solution containing sodium-24, what percentage of the \(^{24}\) Na remains after \(48 \mathrm{h} ?\)