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Chapter 32: Q8CQ (page 1181)
Are some types of cancer more sensitive to radiation than others? If so, what makes them more sensitive?
The dose of radiation is determined by the location of the tumour in the body and its adhesion to healthy cells.
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(a) Calculate the energy released in the neutron-induced fission (similar to the spontaneous fission in Example\(32.3\)) \(n{ + ^{238}}U{ \to ^{96}}Sr{ + ^{140}}Xe + 3n\), given \(m{(^{96}}Sr) = 95.921750{\rm{ }}u\) and \(m{(^{140}}Xe) = 139.92164{\rm{ }}u\).
(b) This result is about \(6{\rm{ }}MeV\) greater than the result for spontaneous fission. Why?
(c) Confirm that the total number of nucleons and total charge are conserved in this reaction.
Verify by listing the number of nucleons, total charge, and electron family number before and after the cycle that these quantities are conserved in the overall proton-proton cycle in \(2{e^ - } + {4^1}H{ \to ^4}He + 2{\nu _e} + 6\gamma \).
The activities of \(^{131}I\) and \(^{123}I\) used in thyroid scans are given in Table \({\rm{32}}{\rm{.1}}\) to be 50 and \(70\mu Ci\), respectively. Find and compare the masses of \(^{131}I\)and \(^{123}I\) in such scans, given their respective half-lives are \({\rm{8}}{\rm{.04\;d}}\)and \({\rm{13}}{\rm{.2\;h}}\). The masses are so small that the radioiodine is usually mixed with stable iodine as a carrier to ensure normal chemistry and distribution in the body.
Two fusion reactions mentioned in the text are
\(n{ + ^3}He{ \to ^4}He + \gamma \)
and
\(n{ + ^1}H{ \to ^2}H + \gamma \).
Both reactions release energy, but the second also creates more fuel. Confirm that the energies produced in the reactions are \(20.58\) and\(2.22{\rm{ }}MeV\), respectively. Comment on which product nuclide is most tightly bound, \(^4He\) or\(^2H\).
(a) Estimate the years that the deuterium fuel in the oceans could supply the energy needs of the world. Assume world energy consumption to be ten times that of the United States which is \(8 \times {10^9}J/y\) and that the deuterium in the oceans could be converted to energy with an efficiency of \(32\% \). You must estimate or look up the amount of water in the oceans and take the deuterium content to be \(0.015\% \) of natural hydrogen to find the mass of deuterium available. Note that approximate energy yield of deuterium is \(3.37 \times {10^{14}}J/kg\).
(b) Comment on how much time this is by any human measure. (It is not an unreasonable result, only an impressive one.)
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