Chapter 16

Why doesn't gamma emission change the elemental identity of a nucleus?

Complete this nuclear reaction, and name the decay process: \({ }_{4}^{8} \mathrm{Be}+? \rightarrow{ }_{3}^{8} \mathrm{Li}\)

Complete this nuclear reaction, and name the decay process: \({ }_{20}^{47} \mathrm{Ca} \rightarrow ?+{ }_{21}^{47} \mathrm{Sc}\)

Complete this nuclear reaction, and name the decay process: \(? \rightarrow{ }_{5}^{11} \mathrm{~B}+{ }_{-1}^{0} \mathrm{e}\)

Suppose you have \(100 \mathrm{~g}\) of \({ }_{53}^{123} \mathrm{I}\). How much of it will be left after \(26.2 \mathrm{~h}\) ? After \(39.3 \mathrm{~h}\) ? [The half-life of \({ }_{53}^{123} \mathrm{I}\) is \(13.1 \mathrm{~h}\).]

Would \({ }_{6}^{14} \mathrm{C}\) be useful in dating a fossil that is 120 million years old? Explain.

For a fission or fusion reaction to be exothermic, what must be true about the mass defects of the products compared to the mass defect of the reactants? Explain fully.

Explain the difference between nuclear fission and nuclear fusion.

Why does nuclear fission often proceed as a chain reaction?

Complete this fusion reaction: \({ }_{4}^{8} \mathrm{Be}+{ }_{2}^{4} \mathrm{He} \rightarrow ?+\gamma\)

The hydrogen in our Sun is undergoing fusion and turning into helium. Billions of years from now, the hydrogen will run out and the helium atoms will fuse, forming heavier atoms. Eventually, these heavier atoms will also fuse. Interestingly, when astronomers examine the remnants of burnt-out stars, they find them to be extremely rich in iron. Explain why this is so.

What is the definition of critical mass?

In a nuclear power plant, what is the job of the heat produced in the fission reactions?

Discuss the benefits and problems associated with using nuclear fission to produce electricity.

Why can't a nuclear reactor explode like a nuclear bomb?

Why are such high temperatures needed to initiate nuclear fusion?

At the end of their life cycles and before they explode into supernovas, the cores of some stars become so hot and dense that they can start to fuse helium atoms together to make heavier elements. How is this fact important given that modern theory tells us that the universe began as mostly hydrogen?

What are the advantages of fusion reactors over fission reactions, and why are there as yet no fusion reactors operating on Earth to generate power?

Of the types of radioactive decay studied in this chapter, which is least likely to damage you upon external exposure? Which is most likely? Explain fully.

How does radiation damage living organisms?

Radioactivity is often called ionizing radiation. Why?

Which has the larger binding energy per mole of nucleons, \({ }_{2}^{4}\) He (molar mass \(4.00150 \mathrm{~g} / \mathrm{mol}\) ) or \({ }_{3}^{6} \mathrm{Li}\) (molar mass \(6.01348 \mathrm{~g} / \mathrm{mol}\) )? [Useful masses: proton, \(1.00730 \mathrm{~g} / \mathrm{mol}\); neutron, \(1.00870 \mathrm{~g} / \mathrm{mol} ;\) electron, \(0.00055 \mathrm{~g} / \mathrm{mol}]\)

Would fusing two \({ }^{56} \mathrm{Fe}\) atoms together to produce \({ }^{112}\) Te be an exothermic reaction or an endothermic reaction? Justify your answer. (Hint: Don't do a calculation, just consult the plot of binding energy versus number of nucleons in the nucleus.)

Consider the radioactive decay of radium to radon: \({ }_{88}^{226} \mathrm{Ra} \rightarrow{ }_{86}^{222} \mathrm{Rn}+?\) (a) Write the complete equation. (b) What type of decay is this? (c) Explain why radium-226 is likely to undergo the type of decay you named in part (b). (d) How much energy is released, in kilojoules, when 1 mole of \({ }^{226}\) Ra decays? [Molar masses: \({ }_{88}^{226} \mathrm{Ra}, 226.0254 \mathrm{~g} / \mathrm{mol} ;{ }_{86}^{222} \mathrm{Rn}, 222.0175 \mathrm{~g} / \mathrm{mol}\) \(\left.{ }_{2}^{4} \mathrm{He}, 4.0026036 \mathrm{~g} / \mathrm{mol}\right]\) (e) How much energy is released, in kilojoules, when \(1 \mathrm{~g}\) of \({ }_{88}^{226}\) Ra decays?

Polonium-210 is an alpha emitter and has a half-life of 138 days. (a) Write the equation for the radioactive decay of polonium-210. (b) How long will it take before only \(5.00 \%\) of the original amount of \({ }^{210}\) Po in a sample remains?

Rubidium- 87, a beta emitter, is a product of positron emission. (a) Identify the parent nucleus of \({ }^{87} \mathrm{Rb}\). (b) When the parent nucleus named in part (a) decays, does the \(\mathrm{n} / \mathrm{p}\) ratio increase or decrease?

Complete these equations representing nuclear reactions: (a) \({ }_{51}^{121} \mathrm{Sb}+{ }_{2}^{4} \mathrm{He} \rightarrow ?+{ }_{1}^{1} \mathrm{H}\) (b) \({ }_{13}^{27} \mathrm{Al}+{ }_{2}^{4} \mathrm{He} \rightarrow ?+{ }_{0}^{1} \mathrm{n}\) (c) \({ }_{92}^{238} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \rightarrow ?+{ }_{-1}^{0} \mathrm{e}\)

Which isotope in each pair is more likely to decay by electron capture? (a) \({ }^{13} \mathrm{~B}\) or \({ }^{8} \mathrm{~B}\) (b) \({ }^{209} \mathrm{Bi}\) or \({ }^{194} \mathrm{Bi}\)

The isotopes \({ }^{17} \mathrm{~F}^{20} \mathrm{~F}\), and \({ }^{21} \mathrm{~F}\) are all radioactive, decaying either by beta emission or by positron emission. Name the decay process for each isotope.

Suppose you discovered a new radioactive decay mode for which the daughter had a mass number seven lower than the parent, and was three places to the left of the parent in the periodic table. What particle(s) would the parent nucleus have to eject to accomplish such a decay?

A painting supposedly by Rembrandt \((1609-\) 1669 was found to contain \(96.1 \%\) of the amount of \({ }^{14} \mathrm{C}\) found in a living plant. Could this painting have been done by Rembrandt? [The half-life of \({ }^{14} \mathrm{C}\) is 5715 years. ] Justify your answer.

Consider the fission reaction \({ }_{0}^{1} \mathrm{n}+{ }_{92}^{235} \mathrm{U} \rightarrow{ }_{37}^{89} \mathrm{Rb}+3{ }_{-1}^{0} \mathrm{e}+3{ }_{0}^{1} \mathrm{n}+?\) (a) What is the missing fission product represented by the question mark? (b) What is it about this reaction that allows for a chain reaction? (c) How much energy, in kilojoules, is released per gram of \({ }^{235} \mathrm{U} ?\) [Molar masses: \({ }^{235} \mathrm{U}, 235.0439 \mathrm{~g} / \mathrm{mol}\) \({ }^{89} \mathrm{Rb}, 88.8913 \mathrm{~g} / \mathrm{mol} ;\) missing product, \(143.8817 \mathrm{~g} / \mathrm{mol} ;{ }_{0}^{1} \mathrm{n}, 1.00870 \mathrm{~g} / \mathrm{mol} ;\) \(\left.{ }_{-1}^{0} \mathrm{e}, 0.00055 \mathrm{~g} / \mathrm{mol}\right]\) (d) How many kilograms of TNT must be detonated to produce the same amount of energy if the energy released per gram of TNT detonated is \(2.76 \mathrm{~kJ}\) ?

Thorium-232 undergoes the following decays successively: parent \({ }^{232}\) Th decays to six alpha particles plus daughter 1, then daughter 1 decays to four beta particles plus daughter \(2 .\) Identify daughter 2 .

In the ore of what metal would you look for thorium? Explain.In the ore of what metal would you look for thorium? Explain.

(a) Write the reaction for the beta decay of tritium. (b) Like \({ }^{14} \mathrm{C}\), tritium is formed by nuclear reactions in the upper atmosphere. What is the missing product here: \({ }_{7}^{14} \mathrm{~N}+{ }_{0}^{1} \mathrm{n} \rightarrow{ }_{1}^{3} \mathrm{H}+?\) (c) The half-life of tritium is only \(12.26\) years, and yet there is always some present on Earth (about 1 atom in every \(10^{18} \mathrm{H}\) atoms is tritium). How can this be?

Polonium-210, an alpha emitter, has a halflife of \(138.4\) days. Suppose you were to collect the helium gas originating from the alpha particles. How many milliliters of helium gas at standard temperature and pressure would you collect from \(1.000 \mathrm{~g}\) of polonium dioxide, \(\mathrm{PoO}_{2}\), in a period of \(138.4\) days? [Assume all the polonium in the sample is \({ }^{210} \mathrm{Po}\), molar mass \(209.98287 \mathrm{~g} / \mathrm{mol}\). Alpha emission from polonium- 210 yields the nonradioactive isotope lead-206; see Problem 16.103.]

Past the "bismuth buoy," \(\beta\) radiation will not render a radioactive nucleus nonradioactive. Explain why.

Consider the nuclear fusion of hydrogen into helium: \(4{ }_{1}^{1} \mathrm{H} \rightarrow{ }_{2}^{4} \mathrm{He}+2\) identical subatomic particles (a) What are the two identical subatomic particles? (b) During this transformation, mass is lost and converted into energy, releasing \(2.56 \times 10^{9} \mathrm{~kJ}\) per mole of helium formed. How many gallons of gasoline would you have to burn to release this much energy, assuming gasoline is pure octane? Burning octane releases \(5509.0 \mathrm{~kJ} / \mathrm{mol} ;\) the \(\mathrm{MM}\) of octane is \(114.23 \mathrm{~g} / \mathrm{mol} ;\) the density of octane is \(0.703 \mathrm{~g} / \mathrm{mL} ;\) there are \(3785.408 \mathrm{~mL}\) per gallon. (c) How much mass was lost in grams? Note that a joule is a \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\).

Given four nuclei: \({ }_{10}^{20} \mathrm{~A},{ }_{9}^{17} \mathrm{~B},{ }_{12}^{28} \mathrm{C}\), and \({ }_{86}^{226} \mathrm{D}\), which is likely to emit a \(\beta^{-}\) particle, and which is likely to emit a \(\beta^{+}\) particle? Explain your choices.

Over time, \(3.00 \mathrm{~g}\) of \({ }_{55}^{132} \mathrm{Cs}\) decays by \(\beta^{-}\) emission to produce stable xenon. If the half-life of \({ }_{55}^{132} \mathrm{Cs}\) is 55 days, how much \({ }_{55}^{132} \mathrm{Cs}\) will be left after 150 days?