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Chapter 32: Q9CQ (page 1181)
Suppose a person swallows some radioactive material by accident. What information is needed to be able to assess possible damage?
We need to know what sort of radioactive element was consumed and how much of it was consumed.
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(a) Calculate the energy released in the neutron-induced fission reaction\(n{ + ^{235}}U{ \to ^{92}}Kr{ + ^{142}}Ba + 2n\),
Given \(m{(^{92}}Kr) = 91.926269{\rm{ }}u\) and
\(m{(^{142}}Ba) = 141.916361{\rm{ }}u\).
(b) Confirm that the total number of nucleons and total charge are conserved in this reaction.
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\(^2H\).
Another set of reactions that result in the fusing of hydrogen into helium in the Sun and especially in hotter stars is called the carbon cycle. It is
\(\begin{array}{*{20}{l}}{^{12}C{ + ^1}H}&{{ \to ^{13}}N + \gamma ,}\\{^{13}N}&{{ \to ^{13}}C + {e^ + } + {v_e},}\\{^{13}C{ + ^1}H}&{{ \to ^{14}}N + \gamma ,}\\{^{14}N{ + ^1}H}&{{ \to ^{15}}O + \gamma ,}\\{^{15}O}&{{ \to ^{15}}N + {e^ + } + {v_e},}\\{^{15}N{ + ^1}H}&{{ \to ^{12}}C{ + ^4}He.}\end{array}\)
Write down the overall effect of the carbon cycle (as was done for the proton-proton cycle in \(2{e^ - } + {4^1}H{ \to ^4}He + 2{v_e} + 6\gamma \)). Note the number of protons (\(^1H\)) required and assume that the positrons (\({e^ + }\)) annihilate electrons to form more \(\gamma \) rays.
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 \(2{e^ - } + {4^1}H{ \to ^4}He + 2{\nu _e} + 6\gamma \).
How many kilograms of water are needed to obtain the \(198.8{\rm{ }}mol\) of deuterium, assuming that deuterium is \(0.01500\% \) (by number) of natural hydrogen?
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