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Chapter 21: Problem 2
What are the steps in balancing nuclear equations?
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Identify two of the most abundant radioactive elements that exist on Earth. Explain why they are still present. (You may need to consult a handbook of chemistry.)
From the definition of curie, calculate Avogadro's number, given that the molar mass of \({ }^{226} \mathrm{Ra}\) is \(226.03 \mathrm{~g} / \mathrm{mol}\) and that it decays with a half-life of \(1.6 \times 10^{3} \mathrm{yr}\)
Fill in the blanks in these radioactive decay series: (a) \(^{232} \mathrm{Th} \stackrel{\alpha}{\longrightarrow}\) _______ \(\stackrel{\beta}{\longrightarrow}\) ________ \(\stackrel{\beta}{\longrightarrow}{ }^{228} \mathrm{Th}\) (b) \({ }^{235} \mathrm{U} \stackrel{\alpha}{\longrightarrow}\) ________ \(\stackrel{\beta}{\longrightarrow}\) _________ \(\stackrel{\alpha}{\longrightarrow}^{227} \mathrm{Ac}\) (c) _______ \(\stackrel{\alpha}{\longrightarrow}{ }^{233} \mathrm{~Pa} \stackrel{\beta}{\longrightarrow}\) ___________ \(\stackrel{\alpha}{\longrightarrow}\) ________.
The radius of a uranium- 235 nucleus is about \(7.0 \times\) \(10^{-3} \mathrm{pm} .\) Calculate the density of the nucleus in \(\mathrm{g} / \mathrm{cm}^{3}\). (Assume the atomic mass is 235 amu.)
(a) What is the activity, in millicuries, of a 0.500 -g sample of \({ }_{93}^{237} \mathrm{~Np}\) ? (This isotope decays by \(\alpha\) -particle emission and has a half-life of \(2.20 \times 10^{6}\) yr.) (b) Write a balanced nuclear equation for the decay of \({ }^{237} \mathrm{~Np}\)
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