Chapter 21

A free neutron is unstable and decays into a proton with a half-life of \(10.4\) min. (a) What other particle forms? (b) Why don't neutrons in atomic nuclei decay at the same rate?

Americium-241 is an alpha emitter used in smoke detectors. The alpha radiation ionizes molecules in an air-filled gap between two electrodes in the smoke detector, leading to current. When smoke is present, the ionized molecules bind to smoke particles and the current decreases; when the current is reduced sufficiently, an alarm sounds. (a) Write the nuclear equation corresponding to the alpha decay of americium-241. (b) Why is an alpha emitter a better choice than a gamma emitter for a smoke detector? (c) In a commercial smoke detector, only \(0.2\) micrograms of americium are present. Calculate the energy that is equivalent to the mass loss of this amount of americium due to alpha radiation. The atomic mass of americium- 241 is \(241.056829\) amu. (d) The half-life of americium- 241 is 432 years; the half life of americium-240 is \(2.12\) days. Why is the 241 isotope a better choice for a smoke detector?

Chlorine has two stable nuclides, \({ }^{35} \mathrm{Cl}\) and \({ }^{37} \mathrm{Cl}\). In contrast, \({ }^{36} \mathrm{Cl}\) is a radioactive nuclide that decays by beta emission. (a) What is the product of decay of \({ }^{36} \mathrm{Cl}\) ? (b) Based on the empirical rules about nuclear stability, explain why the nucleus of \({ }^{36} \mathrm{Cl}\) is less stable than either \({ }^{35} \mathrm{Cl}\) or \({ }^{37} \mathrm{Cl}\)

Nuclear scientists have synthesized approximately 1600 nuclei not known in nature. More might be discovered with heavy-ion bombardment using high-energy particle accelerators. Complete and balance the following reactions, which involve heavy-ion bombardments: (a) \({ }_{3}^{6} \mathrm{Li}+{ }_{29}^{56} \mathrm{Ni} \rightarrow\) ? (b) \(_{20}^{40} \mathrm{Ca}+{ }_{96}^{248} \mathrm{Cm} \ldots{ }_{62}^{147} \mathrm{Sm}+?\) (c) \(_{38}^{88} \mathrm{Sr}+{ }_{36}^{84} \mathrm{Kr} \ldots{ }_{46} 116 \mathrm{Pd}+?\) (d) \({ }_{20}^{40} \mathrm{Ca}+{ }_{92}^{238} \mathrm{U} \cdots{ } \rightarrow \frac{70}{30} \mathrm{Zn}+4_{0}^{1} \mathrm{n}+2 ?\)

The synthetic radioisotope technetium-99, which decays by beta emission, is the most widely used isotope in nuclear medicine. The following data were collected on a sample of \({ }^{99} \mathrm{Tc}\) : $$ \begin{array}{ll} \hline \text { Disintegrations per Minute } & \text { Time (h) } \\ \hline 180 & 0 \\ 130 & 2.5 \\ 104 & 5.0 \\ 77 & 7.5 \\ 59 & 10.0 \\ 46 & 12.5 \\ 24 & 17.5 \\ \hline \end{array} $$ Using these data, make an appropriate graph and curve fit to determine the half-life.

According to current regulations, the maximum permissible dose of strontium-90 in the body of an adult is \(1 \mu \mathrm{Ci}\left(1 \times 10^{-6} \mathrm{Ci}\right) .\) Using the relationship rate \(=k N\), calculate the number of atoms of strontium-90 to which this dose corresponds. To what mass of strontium-90 does this correspond? The half-life for strontium-90 is \(28.8 \mathrm{yr}\)

Methyl acetate \(\left(\mathrm{CH}_{3} \mathrm{COOCH}_{3}\right)\) is formed by the reaction of acetic acid with methyl alcohol. If the methyl alcohol is labeled with oxygen-18, the oxygen-18 ends up in the methyl acetate: Do the \(\mathrm{C}-\mathrm{OH}\) bond of the acid and the \(\mathrm{O}-\mathrm{H}\) bond of the alcohol break in the reaction, or do the \(\mathrm{O}-\mathrm{H}\) bond of the acid and the \(\mathrm{C}-\mathrm{OH}\) bond of the alcohol break? Explain.

An experiment was designed to determine whether an aquatic plant absorbed iodide ion from water. lodine\(131\left(t_{1 / 2}=8.02\right.\) days) was added as a tracer, in the form of iodide ion, to a tank containing the plants. The initial activity of a \(1.00-\mu \mathrm{L}\) sample of the water was 214 counts per minute. After 30 days the level of activity in a \(1.00-\mu \mathrm{L}\) sample was \(15.7\) counts per minute. Did the plants absorb iodide from the water? Explain.

The nuclear masses of \({ }^{7} \mathrm{Be},{ }^{9} \mathrm{Be}\), and \({ }^{10} \mathrm{Be}\) are \(7.0147\), \(9.0100\), and \(10.0113\) amu, respectively. Which of these nuclei has the largest binding energy per nucleon?

The Sun radiates energy into space at the rate of \(3.9 \times 10^{26} \mathrm{~J} / \mathrm{s} .\) (a) Calculate the rate of mass loss from the Sun in \(\mathrm{kg} / \mathrm{s}\) (b) How does this mass loss arise? (c) It is estimated that the Sun contains \(9 \times 10^{56}\) free protons. How many protons per second are consumed in nuclear reactions in the Sun?

The average energy released in the fission of a single uranium- 235 nucleus is about \(3 \times 10^{-11} \mathrm{~J}\). If the conversion of this energy to electricity in a nuclear power plant is \(40 \%\) efficient, what mass of uranium-235 undergoes fission in a year in a plant that produces \(1000 \mathrm{MW}\) (megawatts)? Recall that a watt is \(1 \mathrm{~J} / \mathrm{s}\).

Tests on human subjects in Boston in 1965 and 1966, following the era of atomic bomb testing, revealed average quantities of about \(2 \mathrm{pCi}\) of plutonium radioactivity in the average person. How many disintegrations per second does this level of activity imply? If each alpha particle deposits \(8 \times 10^{-13} \mathrm{~J}\) of energy and if the average person weighs \(75 \mathrm{~kg}\), calculate the number of rads and rems of radiation in 1 yr from such a level of plutonium.

Charcoal samples from Stonehenge in England were burned in \(\mathrm{O}_{2}\), and the resultant \(\mathrm{CO}_{2}\) gas bubbled into a solution of \(\mathrm{Ca}(\mathrm{OH})_{2}\) (limewater), resulting in the precipitation of \(\mathrm{CaCO}_{3}\). The \(\mathrm{CaCO}_{3}\) was removed by filtration and dried. A \(788-\mathrm{mg}\) sample of the \(\mathrm{CaCO}_{3}\) had a radioactivity of \(1.5 \times 10^{-2}\) Bq due to carbon-14. By comparison, living organisms undergo \(15.3\) disintegrations per minute per gram of carbon. Using the half-life of carbon-14, 5715 yr, calculate the age of the charcoal sample.

When a positron is annihilated by combination with an electron, two photons of equal energy result. What is the wavelength of these photons? Are they gamma ray photons?

A 25.0-mLsample of \(0.050 \mathrm{M}\) barium nitrate solution was mixed with \(25.0 \mathrm{~mL}\) of \(0.050 \mathrm{M}\) sodium sulfate solution labeled with radioactive sulfur-35. The activity of the initial sodium sulfate solution was \(1.22 \times 10^{6} \mathrm{~Bq} / \mathrm{mL}\). After the resultant precipitate was removed by filtration, the remaining filtrate was found to have an activity of \(250 \mathrm{~Bq} / \mathrm{mL}\). (a) Write a balanced chemical equation for the reaction that occurred. (b) Calculate the \(K_{s p}\) for the precipitate under the conditions of the experiment.