Chapter 20

Write the following isotopes in hyphenated form (e.g., "carbon-14") (a) \(^{24}_{11} \mathrm{Na}\) (b) \(^{29}_{13} \mathrm{Al}\) (c) \(^{73}_{36} \mathrm{Kr}\) (d) \(^{197}_{77} \mathrm{Ir}\)

Write the following isotopes in nuclide notation \((e.g., \left.^{\prime \prime} \frac{14}{6} \mathrm{C}^{\prime \prime}\right)\) (a) oxygen-14 (b) copper-70 (c) tantalum-175 (d) francium-217

For the following isotopes that have missing information, fill in the missing information to complete the notation (a) \(^{34}_{14} \mathrm{X}\) (b) \(^{36}_{X} \mathrm{P}\) (c) \(^{57}_{X} \mathrm{Mn}\) (d) \(^{121}_{56} \mathrm{X}\)

Write the nuclide notation, including charge if applicable, for atoms with the following characteristics: (a) 25 protons, 20 neutrons, 24 electrons (b) 45 protons, 24 neutrons, 43 electrons (c) 53 protons, 89 neutrons, 54 electrons (d) 97 protons, 146 neutrons, 97 electrons

Calculate the density of the \(^{24}_{12} \mathrm{Mg}\) nucleus in g/mL, assuming that it has the typical nuclear diameter of \(1 \times\) \(10^{-13} \mathrm{cm}\) and is spherical in shape.

What are the two principal differences between nuclear reactions and ordinary chemical changes?

Write a brief description or definition of each of the following: (a) nucleon (b) \(\alpha\) particle (c) \(\beta\) particle (d) positron (e) Y ray (f) nuclide (g) mass number (h) atomic number

Which of the various particles ( \(\alpha\) particles, \(\beta\) particles, and so on) that may be produced in a nuclear reaction are actually nuclei?

Write a balanced equation for each of the following nuclear reactions: (a) the production of \(^{17} \mathrm{O}\) from \(^{14} \mathrm{N}\) by \(\alpha\) particle bombardment (b) the production of \(^{14} \mathrm{C}\) from \(^{14} \mathrm{N}\) by neutron bombardment (c) the production of \(^{233}\) Th from \(^{232}\) Th by neutron bombardment (d) the production of \(^{239} \mathrm{U}\) from \(^{238} \mathrm{U}\) by \(_{1}^{2} \mathrm{H}\) bombardment

Technetium-99 is prepared from \(^{98}\) Mo. Molybdenum- 98 combines with a neutron to give molybdenum- \(99,\) an unstable isotope that emits a \(\beta\) particle to yield an excited form of technetium- 99 , represented as \(^{99} \mathrm{Tc}^{*}\). This excited nucleus relaxes to the ground state, represented as \(^{99} \mathrm{Tc}\), by emitting a \(\mathrm{y}\) ray. The ground state of \(^{99} \mathrm{Tc}\) then emits a \(\beta\) particle. Write the equations for each of these nuclear reactions.

What are the types of radiation emitted by the nuclei of radioactive elements?

What changes occur to the atomic number and mass of a nucleus during each of the following decay scenarios? (a) an \(\alpha\) particle is emitted (b) a \(\beta\) particle is emitted (c) Y radiation is emitted (d) a positron is emitted (e) an electron is captured

What is the change in the nucleus that results from the following decay scenarios? (a) emission of a \(\beta\) particle (b) emission of a \(\beta^{+}\) particle (c) capture of an electron

Which of the following nuclei is most likely to decay by positron emission? Explain your choice. (a) chromium-53 (b) manganese-51 (c) iron-59

The following nuclei do not lie in the band of stability. How would they be expected to decay? Explain your answer. (a) \(^{35}_{15} \mathrm{P}\) (b) \(^{239}_{92} \mathrm{U}\) (c) \(^{38}_{20} \mathrm{Ca}\) (d) \(^{3}_{1} \mathrm{H}\) (e) \(^{245}_{94} \mathrm{Pu}\)

The following nuclei do not lie in the band of stability. How would they be expected to decay? (a) \(^{28}_{15} \mathrm{P}\) (b) \(^{235}_{92} \mathrm{U}\) (c) \(^{37}_{20} \mathrm{Ca}\) (d) \(^{9}_{3} \mathrm{Li}\) (e) \(^{245}_{96} \mathrm{Cm}\)

Define the term half-life and illustrate it with an example.

A \(1.00 \times 10^{-6}-\mathrm{g}\) sample of nobelium, 254 No, has a half-life of 55 seconds after it is formed. What is the percentage of 254 102 No remaining at the following times? (a) 5.0 min after it forms (b) \(1.0 \mathrm{h}\) after it forms

\(^{239}_{} \mathrm{Pu}\) is a nuclear waste byproduct with a half-life of 24,000 y. What fraction of the \(^{239}_{} \mathrm{Pu}\) present today will be present in 1000 y?

The isotope \(^{208} \mathrm{Tl}\) undergoes \(\beta\) decay with a half-life of \(3.1 \mathrm{min}\). (a) What isotope is produced by the decay? (b) How long will it take for \(99.0 \%\) of a sample of pure \(^{208} \mathrm{Tl}\) to decay? (c) What percentage of a sample of pure \(^{208} \mathrm{Tl}\) remains un- decayed after \(1.0 \mathrm{h}\) ?

Technetium-99 is often used for assessing heart, liver, and lung damage because certain technetium compounds are absorbed by damaged tissues. It has a half-life of 6.0 h. Calculate the rate constant for the decay of \(^{99}_{43} \mathrm{Tc}\)

A sample of rock was found to contain \(8.23 \mathrm{mg}\) of rubidium- 87 and \(0.47 \mathrm{mg}\) of strontium- 87 . (a) Calculate the age of the rock if the half-life of the decay of rubidium by \(\beta\) emission is \(4.7 \times 10^{10} \mathrm{y}\). (b) If some 87 \(38 \mathrm{Sr}\) was initially present in the rock, would the rock be younger, older, or the same age as the age calculated in (a)? Explain your answer.

Plutonium was detected in trace amounts in natural uranium deposits by Glenn Seaborg and his associates in 1941. They proposed that the source of this \(^{239} \mathrm{Pu}\) was the capture of neutrons by \(^{238} \mathrm{U}\) nuclei. Why is this plutonium not likely to have been trapped at the time the solar system formed 4.7 \(\times 10^{9}\) years ago?

A \(^{7}_{4} \mathrm{Be}\) atom (mass \(=7.0169\) amu) decays into a \(^{7}_{3} \mathrm{Li}\) atom (mass \(=7.0160\) amu) by electron capture. How much energy (in millions of electron volts, \(\mathrm{MeV}\) ) is produced by this reaction?

A \(^{8}_{5} \mathrm{B}\) atom (mass \(=8.0246\) amu) decays into a \(^{8}_{4} \mathrm{B}\) atom (mass \(=8.0053\) amu) by loss of a \(\beta^{+}\) particle (mass \(=\) 0.00055 amu) or by electron capture. How much energy (in millions of electron volts) is produced by this reaction?

Write a balanced equation for each of the following nuclear reactions: (a) bismuth-212 decays into polonium-212 (b) beryllium- 8 and a positron are produced by the decay of an unstable nucleus (c) neptunium- 239 forms from the reaction of uranium- 238 with a neutron and then spontaneously converts into plutonium-239 (d) strontium-90 decays into yttrium-90

Write a balanced equation for each of the following nuclear reactions: (a) mercury-180 decays into platinum-176 (b) zirconium- 90 and an electron are produced by the decay of an unstable nucleus (c) thorium-232 decays and produces an alpha particle and a radium-228 nucleus, which decays into actinium-228 by beta decay

Write the balanced nuclear equation for the production of the following transuranium elements: (a) berkelium-244, made by the reaction of Am-241 and He-4 (b) fermium- 254 , made by the reaction of \(\mathrm{Pu}-239\) with a large number of neutrons (c) lawrencium-257, made by the reaction of Cf-250 and B-11 (d) dubnium-260, made by the reaction of Cf-249 and N-15

How does nuclear fission differ from nuclear fusion? Why are both of these processes exothermic?

Both fusion and fission are nuclear reactions. Why is a very high temperature required for fusion, but not for fission?

Describe the components of a nuclear reactor.

In usual practice, both a moderator and control rods are necessary to operate a nuclear chain reaction safely for the purpose of energy production. Cite the function of each and explain why both are necessary.

Technetium-99m has a half-life of 6.01 hours. If a patient injected with technetium-99m is safe to leave the hospital once \(75 \%\) of the dose has decayed, when is the patient allowed to leave?

Based on what is known about Radon-222's primary decay method, why is inhalation so dangerous?

Given specimens uranium-232 \(\left(t_{1 / 2}=68.9 \mathrm{y}\right)\) and uranium- \(233\left(t_{1 / 2}=159,200 \mathrm{y}\right)\) of equal mass, which one would have greater activity and why?

Given specimens neon-24 \(\left(t_{1 / 2}=3.38 \mathrm{min}\right)\) and bismuth- \(211\left(t_{1 / 2}=2.14 \mathrm{min}\right)\) of equal mass, which one would have greater activity and why?