Problem 46
Cobalt-60, which undergoes beta decay, has a half-life of \(5.26 \mathrm{yr}\). (a) How many beta particles arc emitted in \(600 \mathrm{~s}\) by a \(3.75-\mathrm{mg}\) sample of \({ }^{60} \mathrm{Co}\) ? (b) What is the activity of the sample in Bq?
Problem 47
The cloth shroud from around a mummy is found to have \(a^{14} \mathrm{C}\) activity of \(9.7\) disintegrations per minute per gram of carbon as compared with living organisms that undergo \(16.3\) disintegrations per minute per gram of carbon. From the halflife for \({ }^{14} \mathrm{C}\) decay, \(5715 \mathrm{yr}\), calculate the age of the shroud.
Problem 48
A wooden artifact from a Chinese temple has a \({ }^{14} \mathrm{C}\) activity of \(38.0\) counts per minute as compared with an activity of \(58.2\) counts per minute for a standard of zero age. From the halflife for \({ }^{14} \mathrm{C}\) decay, \(5715 \mathrm{yr}\), determine the age of the artifact.
Problem 49
Potassium-40 decays to argon-40 with a half-life of \(1.27 \times 10^{9} \mathrm{yr}\), What is the age of a rock in which the mass ratio of \({ }^{40} \mathrm{Ar}\) to \({ }^{40} \mathrm{~K}\) is \(4.2\) ?
Problem 50
The half-life for the process \({ }^{238} \mathrm{U} \longrightarrow{ }^{206} \mathrm{~Pb}\) is \(4.5 \times 10^{9} \mathrm{yr}\). A mineral sample contains \(75.0 \mathrm{mg}\) of \({ }^{239} \mathrm{U}\) and \(18.0 \mathrm{mg}\) of \({ }^{206} \mathrm{~Pb}\). What is the age of the mineral? Energy Changes in Nuclear Reactions (Section 21.6)
Problem 57
How much energy must be supplied to break a single \({ }^{21} \mathrm{Ne}\) nucleus into separated protons and neutrons if the nucleus has a mass of \(20.98846\) amu? What is the nuclear binding energy for \(1 \mathrm{~mol}\) of \({ }^{21} \mathrm{Ne}\) ?
Problem 58
The atomic masses of hydrogen-2 (deuterium), helium-4, and lithium-6 are \(2.014102 \mathrm{amu}_{2} 4.002602 \mathrm{amu}\), and \(6.0151228\) amu, respectively. For cach isotope, calculate (a) the nuclear mass, (b) the nuclear binding energy, (c) the nuclear binding energy per nucleon. (d) Which of these three isotopes has the largest nuclear binding energy per nucleon? Does this agrec with the trends plotted in Figure 21.12?
Problem 59
The atomic masses of nitrogen-14, titanium-48, and xenon-129 are \(13.999234\) amu, \(47.935878\) amu, and \(128.904779\) amu, respectively. For each isotope, calculate (a) the nuclear mass, (b) the nuclear binding energy, (c) the nuclear binding energy per nucleon.
Problem 60
The energy from solar radiation falling on Earth is \(1.07 \times 10^{16} \mathrm{~kJ} / \mathrm{min}\). (a) How much loss of mass from the Sun occurs in one day from just the encrgy falling on Farth? (b) If the energy released in the reaction $$ { }^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{56}^{141} \mathrm{Ba}+{ }_{36}^{92} \mathrm{Kr}+3{ }_{0}^{1} \mathrm{n} $$ \(\left({ }^{235} \mathrm{U}\right.\) nuclear mass, \(234.9935 \mathrm{amu} ;{ }^{141} \mathrm{Ba}\) nuclear mass, \(140.8833 \mathrm{amu} ;{ }^{92} \mathrm{Kr}\) nuclear mass, 91.9021 amu) is taken as typical of that occurring in a nuclear reactor, what mass of uranium-235 is required to equal \(0.10 \%\) of the solar energy that falls on Earth in \(1.0\) day?
Problem 61
Based on the following atomic mass values - \({ }^{1} \mathrm{H}, 1.00782\) amu; \({ }^{2} \mathrm{H}, 2.01410 \mathrm{amu} ;{ }^{3} \mathrm{H}, 3.01605 \mathrm{amu} ;{ }^{3} \mathrm{He}, 3.01603 \mathrm{amu} ;\) \({ }^{4} \mathrm{He}, 4.00260 \mathrm{amu}-\) and the mass of the neutron given in the text, calculate the energy released per mole in each of the following nuclear reactions, all of which are possibilities for a controlled fusion process: (a) \({ }_{1}{ }_{1} \mathrm{H}+{ }_{1}^{3} \mathrm{H} \longrightarrow{ }_{2}^{4} \mathrm{He}+{ }_{0}^{1} \mathrm{n}\) (b) \({ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \longrightarrow{ }_{2}^{3} \mathrm{He}+{ }_{0}^{1} \mathrm{n}\) (c) \({ }_{1}^{2} \mathrm{H}+{ }_{2}^{3} \mathrm{He} \longrightarrow{ }_{2}^{4} \mathrm{He}+{ }_{1}^{1} \mathrm{H}\) \(21.53\) Which of the following nuclei is likely to have the largest mass defect per nucleon: (a) \({ }^{59} \mathrm{Co}\), (b) \({ }^{11} \mathrm{~B}\), (c) \({ }^{118} \mathrm{Sn}\), (d) \({ }^{243} \mathrm{Cm}\) ? Explain your answer.
