Problem 2
What do you understand by the terms: (a) atomic number; (b) mass number; (c) mass defect; (d) binding energy per nucleon?
Problem 4
Radium-224 is radioactive and decays by emitting an \(\alpha\) -particle. (a) Write an equation for this process. (b) The decay of radium-224 produces helium gas. Rutherford and Geiger determined that \(\alpha\) -particles were emitted from \(^{224} 88 \mathrm{Ra}\) at a rate of \(7.65 \times 10^{12} \mathrm{s}^{-1} \mathrm{mol}^{-1}\), and that this corresponded to a rate of helium production of \(2.90 \times 10^{-10} \mathrm{dm}^{3} \mathrm{s}^{-1}\) at \(273 \mathrm{K}, 1\) bar. If 1 mole of helium occupies \(22.7 \mathrm{dm}^{3}(273 \mathrm{K}, 1 \mathrm{bar})\), estimate a value for the Avogadro constant.
Problem 5
Use the following data to determine the half-life of \(^{218} 80\) and the rate constant for the decay of \(^{218} 84\) Po. $$\begin{array}{lllllll} \hline \text { Time } / \mathrm{s} & 0 & 200 & 400 & 600 & 800 & 1000 \\ \text { Moles }_{84}^{218} \mathrm{Po} & 0.250 & 0.110 & 0.057 & 0.025 & 0.012 & 0.005 \\ \hline \end{array}$$
Problem 6
The half-life of strontium-90 is 29.1 years. Determine the rate constant for the decay of strontium-90 in units of \(s^{-1}\) [The SI unit of time is the second.]
Problem 9
Interpret the following notational forms of nuclear reactions: (a) \(\frac{58}{26} \mathrm{Fe}(2 \mathrm{n}, \beta)_{27}^{60} \mathrm{Co} ;(\mathrm{b}) \frac{55}{25} \mathrm{Mn}(\mathrm{n}, \gamma)_{25}^{56} \mathrm{Mn}\) \((\mathrm{c})_{16}^{32} \mathrm{S}(\mathrm{n}, \mathrm{p})_{15}^{32} \mathrm{P}\) (d) 233 11 \(\mathrm{Na}(\gamma, 3 \mathrm{n})_{11}^{20} \mathrm{Na}\)
Problem 10
Identify the second fission product in the following reactions: (a) \(\frac{235}{92} \mathrm{U}+_{0}^{1} \mathrm{n}--^{142} \mathrm{s} \mathrm{Ba}+?+2_{0}^{1} \mathrm{n}\) (b) \(\frac{235}{92} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow_{52}^{137} \mathrm{Te}+?+2_{0}^{1} \mathrm{n}\)
Problem 12
Determine the half-life of Bk given that a plot of \(\ln N\) against \(t\) is linear with a gradient of -0.0023 day \(^{-1}\) where \(N\) is the number of nuclides present at time \(t\)
Problem 14
If the oxide \(P_{4} O_{6}\) is dissolved in an aqueous solution of sodium carbonate, compound A of formula \(\mathrm{Na}_{2} \mathrm{HPO}_{3}\) may be crystallized from solution. The IR spectrum of \(\mathbf{A}\) contains a band at \(2300 \mathrm{cm}^{-1}\). The corresponding band in the IR spectrum of \(\mathbf{B}\) (obtained by an analogous method from \(\mathrm{P}_{4} \mathrm{O}_{6}\) and \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) dissolved in \(\mathrm{D}_{2} \mathrm{O}\) ) is at \(1630 \mathrm{cm}^{-1}\) On recrystallization of A from \(\mathrm{D}_{2} \mathrm{O}\), however, its IR spectrum is not affected. Discuss the interpretation of these observations.
Problem 15
For problems 3.15 and \(3.16,\) you may need to refer to Section 7.9 for information on solubility. Why is the method of isotope dilution analysis used to determine the solubility of sparingly soluble salts rather than a method depending upon mass determination?
Problem 16
A small amount of the radioactive isotope \(^{212} 82\) was mixed with a quantity of a non-radioactive lead salt containing \(0.0100 \mathrm{g}\) lead \(\left(A_{\mathrm{r}}=207\right) .\) The whole sample was dissolved in aqueous solution and lead(II) chromate (PbCrO \(_{4}\) ) was precipitated by the addition of a soluble chromate salt. Evaporation of \(10 \mathrm{cm}^{3}\) of the supernatant liquid gave a residue having a radioactivity of \(4.17 \times 10^{-5}\) that of the original quantity of \(^{212} 82\) P. Calculate the solubility of lead(II) chromate in moldm \(^{-3}\)
