Chapter 18: Problem 48
Which has the larger binding energy, \(\mathrm{K}-40\) or \(\mathrm{Ca}-40 ?\) Show by calculation.
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It is possible to estimate the activation energy for fusion by calculating the energy required to bring two deuterons close enough to one another to form an alpha particle. This energy can be obtained by using Coulomb's law in the form \(E=8.99 \times 10^{9} \mathrm{q}_{1} q_{2} / r,\) where \(q_{1}\) and \(q_{2}\) are the charges of the deuterons \(\left(1.60 \times 10^{-19} \mathrm{C}\right), r\) is the radius of the \(\mathrm{He}\) nucleus, about \(2 \times 10^{-15} \mathrm{~m},\) and \(E\) is the energy in joules. (a) Estimate \(E\) in joules per alpha particle. (b) Using the equation \(E=m v^{2} / 2\), estimate the velocity (meters per second) each deuteron must have if a collision between the two of them is to supply the activation energy for fusion \((m\) is the mass of the deuteron in kilograms).
To measure the volume of the blood in an animal's circulatory system, the following experiment was performed. A \(5.0-\mathrm{mL}\) sample of an aqueous solution containing \(1.7 \times 10^{5}\) counts per minute (cpm) of tritium was injected into the bloodstream. After an adequate period of time to allow for the complete circulation of the tritium, a 5.0 -mL sample of blood was withdrawn and found to have \(1.3 \times 10^{3} \mathrm{cpm}\) on the scintillation counter. Assuming that only a negligible amount of tritium has decayed during the experiment, what is the volume of the animal's circulatory system?
Phosphorus-32 is used in biochemical studies to follow the pathway taken by metabolites. Its half-life is 14.3 days. A vial containing \(10.0 \mu \mathrm{g}\left(1 \mu \mathrm{g}=1 \times 10^{-6} \mathrm{~g}\right)\) of \(\mathrm{P}-32\) is acci- dentally spilled into a sink. (a) How long will it take P-32 in the drain to exhibit \(68 \%\) of its original activity? (b) How many atoms of P-32 remain in the sink after 755 days?
To determine the \(K_{\mathrm{sp}}\) value of \(\mathrm{Hg}_{2} \mathrm{I}_{2},\) a solid sample is used, in which some of the iodine is present as radioactive I-131. The count rate of the sample is \(5.0 \times 10^{11}\) counts per minute per mole of \(\mathrm{I}\). An excess amount of \(\mathrm{Hg}_{2} \mathrm{I}_{2}(s)\) is placed in some water, and the solid is allowed to come to equilibrium with its respective ions. A 150.0 -mL sample of the saturated solution is withdrawn and the radioactivity measured at 33 counts per minute. From this information, calculate the \(K_{\mathrm{sp}}\) value for \(\mathrm{Hg}_{2} \mathrm{I}_{2}\).
For Al-28, calculate (a) the mass defect. (b) the binding energy in \(\mathrm{kJ} / \mathrm{mol}\).
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