Chapter 15

Identify the particle given off when a nucleus undergoes \(\alpha\) decay. Identify the particle given off during \(\beta\) decay. Describe the relationship between \(\gamma\) rays and other forms of electromagnetic radiation.

Define the terms atomic number, mass number, nuclide, nucleon, and nucleus.

Define the terms isotopes, isobars, and isotones. Give examples of pairs of nuclides that would be described by each of these terms.

Calculate the number of electrons, protons, and neutrons in a neutral \({ }^{90} \mathrm{Sr}\) atom.

Calculate the number of electrons, protons, and neutrons in both a \({ }^{40} \mathrm{~K}^{+}\) and an \({ }^{127} \mathrm{I}^{-}\) ion.

Explain why the three forms of \(\beta\) decay interconvert isobars.

In theory, \(\beta\) decay could include reactions in which a positron is captured and the charge on the nucleus increases. Explain why the following positron capture reaction does not occur under "normal" conditions. $$ { }_{6}^{14} \mathrm{C}+{ }_{+1} e \longrightarrow{ }_{7}^{14} \mathrm{~N}+h \nu $$

Which of the following reactions interconvert isotopes? Which interconvert isobars? Which interconvert isotones? (a) electron emission (b) electron capture (c) positron emission (d) \(\alpha\) emission (e) neutron emission (f) neutron absorption (g) \(\alpha\) emission followed by two \(\beta^{-}\) decays

Identify the missing particle in each of the following equations and name the form of radioactive decay. (a) \({ }_{53}^{125} \mathrm{I}+{ }_{-1}^{0} e \longrightarrow X\) (b) \({ }_{94}^{240} \mathrm{Pu} \longrightarrow X+{ }_{58}^{144} \mathrm{Ce}+2{ }_{0}^{1} n\) (c) \({ }_{38}^{90} \mathrm{Sr} \longrightarrow X+{ }_{-1}^{0} e\) (d) \({ }_{19}^{40} \mathrm{~K} \longrightarrow X+{ }_{+1}^{0} e\) (e) \({ }_{90}^{228} \mathrm{Th} \longrightarrow X+{ }_{2}^{4} \mathrm{He}\)

Write a balanced equation for the \(\beta\) -particle decay of the \({ }^{99}\) Mo nuclide.

Write a balanced equation for the \(\alpha\) -particle decay of the \({ }^{248}\) Cf nuclide.

Write a balanced equation for the electron capture reaction of the \({ }^{62} \mathrm{Cu}\) nuclide.

Write a balanced equation for the positron emission reaction of the \({ }^{34} \mathrm{Cl}\) nuclide.

Predict the products of the following nuclear reactions. (a) electron emission by \({ }^{32} \mathrm{P}\) (b) positron emission by \({ }^{11} \mathrm{C}\) (c) \(\alpha\) decay by \({ }^{212} \mathrm{Rn}\) (d) electron capture by \({ }^{125} \mathrm{Xe}\)

Predict the products of the following nuclear reactions. (a) \({ }^{208} \mathrm{~Pb}\left({ }_{1}^{2} \mathrm{H}, n\right)\) (b) \({ }_{42}^{95} \mathrm{Mo}(n, \gamma)\) (c) \({ }_{84}^{202} \operatorname{Po}\left({ }_{10}^{22} \mathrm{Ne}, 4 n\right)\) (d) \({ }_{7}^{14} \mathrm{~N}(n, p)\)

Explain why neutron-rich nuclides become more stable when they undergo decay by electron \(\left(\beta^{-}\right)\) emission.

Explain why neutron-poor nuclides become more stable when they undergo decay by either electron capture, positron \(\left(\beta^{+}\right)\) emission, the emission of an alpha particle, or spontaneous fission.

Which of the following nuclides are most likely to be neutron-poor? (a) \({ }^{3} \mathrm{H}\) (b) \({ }^{11} \mathrm{C}\) (c) \({ }^{14} \mathrm{~N}\) (d) \({ }^{40} \mathrm{~K}\) (e) \({ }^{61} \mathrm{Cu}\)

Which isotope of carbon is most likely to decay by positron emission? (a) \({ }^{11} \mathrm{C}\) (b) \({ }^{12} \mathrm{C}\) (c) \({ }^{13} \mathrm{C}\) (d) \({ }^{14} \mathrm{C}\)

Which isotope of carbon is most likely to decay by electron emission? (a) \({ }^{11} \mathrm{C}\) (b) \({ }^{12} \mathrm{C}\) (c) \({ }^{13} \mathrm{C}\) (d) \({ }^{14} \mathrm{C}\)

Calculate the energy released in the following reaction. $$ { }^{10} \mathrm{~B}(n, \alpha)^{7} \mathrm{Li} $$ Use the following data for the masses of the particles involved in the reaction: \({ }^{10} \mathrm{~B}=10.0129 \mathrm{amu} ;{ }^{7} \mathrm{Li}=\) \(7.01600 \mathrm{amu} ;{ }^{4} \mathrm{He}=4.00260 \mathrm{amu}\). Explain why the abil- ity of \({ }^{10} \mathrm{~B}\) to release a high-energy \(\alpha\) particle after it absorbs a thermal neutron generated considerable interest in getting boron compounds to absorb preferentially into the fastgrowing tumor in patients who suffer from brain tumors.

The half-life of \({ }^{32} \mathrm{P}\) is 14.3 days. Calculate how long it would take for a 1.000 -gram sample of \({ }^{32} \mathrm{P}\) to decay to each of the following quantities of \({ }^{32} \mathrm{P}\). (a) 0.500 gram (b) 0.250 gram (c) 0.125 gram

Calculate the half-life for the decay of \({ }^{39} \mathrm{Cl}\) if a \(1.000-\) gram sample decays to 0.125 gram in 165 minutes.

Calculate the rate constants in \(\mathrm{s}^{-1}\) for the decay of the following nuclides from their half-lives. (a) \({ }^{18} \mathrm{~F}, 110\) minutes (b) \({ }^{54} \mathrm{Mn}, 312\) days (c) \({ }^{3} \mathrm{H}, 12.26\) years (d) \({ }^{14} \mathrm{C}, 5730\) years (e) \({ }^{129} \mathrm{I}, 1.6 \times 10^{7}\) years

A 1.000 -gram sample of \({ }^{22} \mathrm{Na}\) decays to 0.20 gram in 6.04 years. Calculate the half-life for this decay, the rate constant, and the time it would take for this sample to decay to 0.075 gram.

Calculate the time required for a 2.50 -gram sample of \({ }^{51} \mathrm{Cr}\) to decay to 1.00 gram, assuming that the half-life is 27.8 days.

A sample of \({ }^{210}\) Po initially weighed 2.000 grams. After 25 days, 0.125 gram of \({ }^{210}\) Po remained, the rest of the sample having decayed to the stable \({ }^{206} \mathrm{~Pb}\) isotope. Calculate the half-life of \(^{210}\) Po and the mass of \(^{206} \mathrm{~Pb}\) formed.

Forgeries that had been accepted by art authorities as paintings by the Dutch artist Vermeer (1632-1675) have been detected by measuring the activity of the \({ }^{210} \mathrm{~Pb}\) isotope in the lead paints. When lead is extracted from its ores, it is separated from \({ }^{226} \mathrm{Ra}\), which is the source of the \({ }^{210} \mathrm{~Pb}\) isotope. The amount of \({ }^{210} \mathrm{~Pb}\) in the paint therefore decreases with time. If the half-life for the decay of \({ }^{210} \mathrm{~Pb}\) is 21 years, what fraction of the \({ }^{210} \mathrm{~Pb}\) would be present in a 300 -year-old painting? What fraction would remain in a 10 -year-old forgery?

The threat to people's health from radon in the air trapped in their houses has received attention in recent years. If the average level of radon in a house is approximately 1 picocurie (pCi) per liter of air, how many radon atoms are there per liter? (Assume that \({ }^{222} \mathrm{Rn}\) is the principal source of this activity and that the half-life for the decay of this nuclide is 3.823 days.)

Calculate the number of disintegrations per minute in a \(1.00-\mathrm{mg}\) sample of \({ }^{238} \mathrm{U}\), assuming that the half-life is \(4.47 \times 10^{9}\) years.

The \({ }^{14} \mathrm{C}\) in living matter has an activity of 15.3 disintegrations, or "counts," per minute (cpm). What is the age of an artifact that has an activity of \(4 \mathrm{cpm} ?\left({ }^{14} \mathrm{C}: t_{1 / 2}=5730 \mathrm{yr}\right)\)

Measurements on the linen wrappings from the Book of Isaiah in the Dead Sea Scrolls suggest that the scrolls contain about \(79.5 \%\) of the \({ }^{14} \mathrm{C}\) expected in living tissue. How old are these scrolls? \(\left({ }^{14} \mathrm{C}: t_{1 / 2}=5730 \mathrm{yr}\right)\)

The Lascaux cave near Montignac in France contains a series of remarkable cave paintings. Radiocarbon dating of charcoal taken from this site suggests an age of 15,520 years. What fraction of the \({ }^{14} \mathrm{C}\) present in living tissue is still present in this sample? \(\left({ }^{14} \mathrm{C}: t_{1 / 2}=5730 \mathrm{yr}\right)\)

Charcoal samples from Stonehenge in England emit \(62.3 \%\) of the disintegrations per gram of carbon per minute expected for living tissue. What is the age of this charcoal? \(\left({ }^{14} \mathrm{C}: t_{1 / 2}=5730 \mathrm{yr}\right)\)

A lump of beeswax was excavated in England near a collection of Bronze Age objects that are between 2500 and 3000 years old. Radiocarbon analysis of the beeswax suggests an activity roughly \(90.3 \%\) of that observed for living tissue. Was this beeswax part of the hoard of Bronze Age objects, or did it date from another period? \(\left({ }^{14} \mathrm{C}: t_{1 / 2}=5730 \mathrm{yr}\right)\)

Use Lewis structures to describe the difference between an \(\mathrm{H}_{2} \mathrm{O}^{+}\) ion and an \(\mathrm{H}_{3} \mathrm{O}^{+}\) ion. If a free radical is an ion or molecule that contains one or more unpaired electrons, which of these ions is a free radical?

Explain why sources of \(\alpha\) particles are intrinsically more dangerous than sources of \(\beta^{-}\) particles.

The first artificial radioactive elements were synthesized by Irene Curie and Frederic Joliot, who bombarded \({ }^{10} \mathrm{~B}\) and \({ }^{27} \mathrm{Al}\) with a particles to form \({ }^{13} \mathrm{~N}\) and \({ }^{30} \mathrm{P}\). Write balanced equations for these reactions, identify the particle ejected in each reaction, and predict the mode of decay expected for the products of these reactions.

Russell, Soddy, and Fajans predicted that the emission of one \(\alpha\) and two \(\beta\) particles by a nuclide would produce an isotope of the parent nuclide. Which isotope of \({ }^{216} \mathrm{Po}\) is produced by such decay? What intermediate nuclides are formed?

In the first synthesis of an isotope of mendelevium \((Z=\) 101), Ghiorso and co-workers bombarded \({ }^{253}\) Es with \(\alpha\) particles. Starting with less than \(10^{-12}\) gram of einsteinium, they isolated one atom of mendelevium after a period of a few hours. If a neutron was emitted in this reaction, what isotope of Md was produced? Another isotope of mendelevium was produced by bombarding \({ }^{238} \mathrm{U}\) with \({ }^{19} \mathrm{~F}\) atoms. If five neutrons were ejected in this reaction, what isotope of Md was produced?

How many alpha and beta particles are emitted when \({ }^{232}\) Th decays to \({ }^{208} \mathrm{~Pb}\) ?

Explain why relatively light nuclides give off energy when they fuse to form heavier nuclides, whereas relatively heavy nuclides give off energy when they undergo fission.

Describe the difference between spontaneous and induced fission reactions. Explain why nuclei undergoing induced fission reactions have much shorter half-lives.

Describe the advantages and disadvantages of fusion reactors versus fission reactors.

Describe the difference between the s-process and r-process for the synthesis of nuclides. Explain why the s-process can't synthesize relatively heavy naturally occurring nuclides, \(\operatorname{such} \mathrm{as}{\underline{\phantom{xx}}}^{238} \mathrm{U}\).

The activity of the \({ }^{14} \mathrm{C}\) in living tissue is 15.3 disintegrations per minute per gram of carbon. The limit for reliable determination of \({ }^{14} \mathrm{C}\) ages is 0.10 disintegration per minute per gram of carbon. Calculate the maximum age of a sample that can be dated accurately by radiocarbon dating if the half-life for the decay of \({ }^{14} \mathrm{C}\) is 5730 years.

Use the relationship between the energy and the frequency of a photon to calculate the energy in kilojoules per mole of a photon of blue light that has a frequency of \(6.5 \times 10^{14} \mathrm{~s}^{-1}\). Compare the results of this calculation with the ionization energy of water \((1216 \mathrm{~kJ} / \mathrm{mol})\).

Calculate the energy in kilojoules per mole for an \(\mathrm{X}\) ray that has a frequency of \(3 \times 10^{17} \mathrm{~s}^{-1}\). How do the results of this calculation compare with the ionization energy of water \((1216 \mathrm{~kJ} / \mathrm{mol}) ?\)