Problem 35
Complete and balance the following nuclear equations by supplying the missing particle: (a) \({ }_{58}^{252} \mathrm{Cf}+{ }_{5}^{10} \mathrm{~B} \longrightarrow 3{ }_{0}^{1} \mathrm{n}+\) ? (b) \({ }_{1}^{2} \mathrm{H}+{ }_{2}^{3} \mathrm{He} \longrightarrow{ }_{2}^{4} \mathrm{He}+\) ? (c) \({ }_{1}^{1} \mathrm{H}+{ }_{5}^{11} \mathrm{~B} \longrightarrow 3\) ? (d) \({ }_{53}^{122} \mathrm{I} \longrightarrow{ }_{54}^{122} \mathrm{Xe}+\) ? (e) \({ }_{26}^{59} \mathrm{Fe} \longrightarrow{ }_{-1}^{0} \mathrm{e}+\) ?
Problem 36
Complete and balance the following nuclear equations by supplying the missing particle: (a) \({ }_{7}^{14} \mathrm{~N}+{ }_{2}^{4} \mathrm{He} \longrightarrow\) ? \(+{ }_{1}^{1} \mathrm{H}\) (b) \({ }_{19}^{40} \mathrm{~K}+{ }_{-1}^{0} \mathrm{c}\) (orbital electron) \(\longrightarrow\) ? (c) \(?+{ }_{2}^{4} \mathrm{He} \longrightarrow{ }_{14}^{30} \mathrm{Si}+{ }_{1}^{1} \mathrm{H}\) (d) \({ }_{26}^{58} \mathrm{Fe}+2{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{27}^{60} \mathrm{Co}+\) ? (e) \({ }_{42}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{54}^{135} \mathrm{Xe}+2{ }_{0}^{1} \mathrm{n}+\) ?
Problem 37
Write balanced equations for (a) \({ }_{92}^{238} \mathrm{U}(\alpha, \mathrm{n})_{{ }_{94}^{24}}^{24} \mathrm{Pu}\), (b) \({ }_{7}^{14} \mathrm{~N}(\alpha, \mathrm{p})_{8}^{17} \mathrm{O},(\mathrm{c}){ }_{26}^{56} \mathrm{Fe}\left(\alpha, \beta^{-}\right)_{29}^{60} \mathrm{Cu}\).
Problem 38
Write balanced equations for each of the following nuclear reactions: (a) \({ }_{92}^{238} \mathrm{U}(\mathrm{n}, \gamma){ }_{92}^{239} \mathrm{U},(\mathrm{b}){ }_{8}^{16} \mathrm{O}(\mathrm{p}, \alpha){ }_{7}^{13} \mathrm{~N}\), (c) \({ }_{8}^{18} \mathrm{O}(\mathrm{n}, \beta){ }_{9}^{19} \mathrm{~F}\). Rates of Radioactive Decay (Section 21.4)
Problem 39
Each statement that follows refers to a comparison between two radioisotopes, \(A\) and \(X\). Indicate whether each of the following statements is true or false, and why. (a) If the half-life for \(\mathrm{A}\) is shorter than the half-life for \(\mathrm{X}, \mathrm{A}\) has a larger decay rate constant. (b) If \(X\) is "not radioactive," its half-life is essentially zero. (c) If A has a half-life of \(10 \mathrm{yr}\), and \(\mathrm{X}\) has a half-life of \(10,000 \mathrm{yr}\), A would be a more suitable radioisotope to measure processes occurring on the 40 -yr time scale.
Problem 40
It has been suggested that strontium-90 (generated by nuclear testing) deposited in the hot desert will undergo radioactive decay more rapidly because it will be exposed to much higher average temperatures. (a) Is this a reasonable suggestion? (b) Does the process of radioactive decay have an activation energy, like the Arrhenius behavior of many chemical reactions (Section 14.5)?
Problem 41
Some watch dials are coated with a phosphor, like ZnS, and a polymer in which some of the \({ }^{1} \mathrm{H}\) atoms have been replaced by \({ }^{3} \mathrm{H}\) atoms, tritium. The phosphor emits light when struck by the beta particle from the tritium decay, causing the dials to glow in the dark. The half-life of tritium is \(12.3 \mathrm{yr}\). If the light given off is assumed to be directly proportional to the amount of tritium, by how much will a dial be dimmed in a watch that is 50 yr old?
Problem 42
It takes \(4 \mathrm{~h} \mathrm{} 39 \mathrm{~min}\) for a \(2.00\)-mg sample of radium-230 to decay to \(0.25 \mathrm{mg}\). What is the half-life of radium-230?
Problem 43
Cobalt-60 is a strong gamma emitter that has a half-life of \(5.26 \mathrm{yr}\). The cobalt- 60 in a radiotherapy unit must be replaced when its radioactivity falls to \(75 \%\) of the original sample. If an original sample was purchased in June 2013, when will it be necessary to replace the cobalt-60?
Problem 44
How much time is required for a \(6.25-\mathrm{mg}\) sample of \({ }^{51} \mathrm{Cr}\) to decay to \(0.75 \mathrm{mg}\) if it has a half-life of \(27.8\) days?
