Chapter 19: Problem 49
How does a hydrogen bomb work?
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
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Chapter 19: Problem 49
How does a hydrogen bomb work?
These are the key concepts you need to understand to accurately answer the question.
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A radioactive substance undergoes decay as follows: $$\begin{array}{cc}\hline \text { Time (days) } & \text { Mass (g) } \\\\\hline 0 & 500 \\\1 & 389 \\\2 & 303 \\\3 & 236 \\\4 & 184 \\\5 & 143 \\\6 & 112 \\\\\hline\end{array}$$ Calculate the first-order decay constant and the halflife of the reaction.
(a) Assuming nuclei are spherical in shape, show that its radius \((r)\) is proportional to the cube root of mass number \((A) .(\mathrm{b})\) In general, the radius of a nucleus is given by \(r=r_{0} A^{\frac{1}{3}},\) where \(r_{0},\) the proportionality constant, is given by \(1.2 \times 10^{-15} \mathrm{~m}\). Calculate the volume of the \({ }^{238} \mathrm{U}\) nucleus.
Complete the following nuclear equations and identify \(\mathrm{X}\) in each case: (a) \({ }_{12}^{26} \mathrm{Mg}+{ }_{1}^{1} \mathrm{p} \longrightarrow{ }_{2}^{4} \alpha+\mathrm{X}\) (b) \({ }_{27}^{59} \mathrm{Co}+{ }_{1}^{2} \mathrm{H} \longrightarrow{ }_{27}^{60} \mathrm{Co}+\mathrm{X}\) (c) \({ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{36}^{94} \mathrm{Kr}+{ }_{56}^{139} \mathrm{Ba}+3 \mathrm{X}\) (d) \({ }_{24}^{53} \mathrm{Cr}+{ }_{2}^{4} \alpha \longrightarrow{ }_{0}^{1} \mathrm{n}+\mathrm{X}\) (e) \({ }_{8}^{20} \mathrm{O} \longrightarrow{ }_{9}^{20} \mathrm{~F}+\mathrm{X}\).
Define nuclear binding energy, mass defect, and nucleon.
Calculate the energy released (in joules) from the following fusion reaction: $${ }_{1}^{2} \mathrm{H}+{ }_{1}^{3} \mathrm{H} \longrightarrow{ }_{2}^{4} \mathrm{He}+{ }_{0}^{1} \mathrm{n}$$ The atomic masses are \({ }_{1}^{2} \mathrm{H}=2.0140 \mathrm{amu},{ }_{1}^{3} \mathrm{H}=3.01603\) \(\mathrm{amu},{ }_{2}^{4} \mathrm{He}=4.00260 \mathrm{amu},{ }_{0}^{1} \mathrm{n}=1.008665 \mathrm{amu}\).
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