Chapter 20

Which of the following poses a greater health hazard: a radioactive isotope with a short half-life or a radioactive isotope with a long half-life? Explain. [Assume the same type of radiation $(\alpha$ or $\beta )$ and comparable energetics per particle emitted.]

A radioactive isotope of copper decays as follows: $${}^{64}\mathrm{Cu}⟶{}^{64}\mathrm{Zn}+{}_{-1}^0\beta t_{1/2}=12.8$$ Starting with $84.0\mathrm{g}$ of ${}^{64}\mathrm{Cu},$ calculate the quantity of ${}^{64}\mathrm{Zn}$ produced after $18.4\mathrm{h}.$

A 0.0100 -g sample of a radioactive isotope with a halflife of $1.3\times {10}^9$ years decays at the rate of $2.9\times {10}^4$ disintegrations per minute. Calculate the molar mass of the isotope.

The half-life of ${}^{27}\mathrm{Mg}$ is $9.50\min .$ (a) Initially there were $4.20\times {10}^{1227}\mathrm{Mg}$ nuclei present. How many ${}^{27}\mathrm{Mg}$ nuclei are left 30.0 min later? (b) Calculate the ${}^{27}\mathrm{Mg}$ activities (in Ci) at $t=0$ and $t=30.0$ min. (c) What is the probability that any one ${}^{27}\mathrm{Mg}$ nucleus decays during a 1 -s interval? What assumption is made in this calculation?

During the past two decades, syntheses of elements 110 through 118 have been reported. Element 110 was created by bombarding ${}^{208}\mathrm{Pb}$ with ${}^{62}\mathrm{Ni}$, element 111 was created by bombarding ${}^{209}\mathrm{Bi}$ with ${}^{64}\mathrm{Ni}$, element 112 was created by bombarding ${}^{208}\mathrm{Pb}$ with ${}^{66}\mathrm{Zn}$, element 114 was created by bombarding ${}^{244}\mathrm{Pu}$ with ${}^{48}\mathrm{Ca}$, element 115 was created by bombarding ${}^{243}\mathrm{Am}$ with ${}^{48}\mathrm{Ca}$, element 116 was created by bombarding ${}^{248}\mathrm{Cm}$ with ${}^{48}\mathrm{Ca},$ element 117 was created by bombarding ${}^{249}\mathrm{Bk}$ with ${}^{48}\mathrm{Ca},$ and element 118 was created by bombarding ${}^{249}\mathrm{Cf}$ with ${}^{48}\mathrm{Ca}$. Write an equation for each synthesis and predict the chemical properties of these elements.

Explain why achievement of nuclear fusion in the laboratory requires a temperature of about 100 million degrees Celsius, which is much higher than that in the interior of the sun ( 15 million degrees Celsius).

An electron and a positron are accelerated to nearly the speed of light before colliding in a particle accelerator. The resulting collision produces an exotic particle having a mass many times that of a proton. Does this result violate the law of conservation of mass? Explain.

The constituents of wine contain, among others, carbon, hydrogen, and oxygen atoms. A bottle of wine was sealed about 6 years ago. To confirm its age, which of the isotopes would you choose in a radioactive dating study? The half-lives of the isotopes are: ${}^{14}\mathrm{C}:5715$ years; ${}^{15}\mathrm{O}:124\mathrm{s};{}^3\mathrm{H}:12.5$ years. Assume that the activities of the isotopes were known at the time the bottle was sealed.

To detect bombs that may be smuggled onto airplanes, the Federal Aviation Administration (FAA) will soon require all major airports in the United States to install thermal neutron analyzers. The thermal neutron analyzer will bombard baggage with low-energy neutrons, converting some of the nitrogen- 14 nuclei to nitrogen-15, with simultaneous emission of $\gamma$ rays. Because nitrogen content is usually high in explosives, detection of a high dosage of $\gamma$ rays will suggest that a bomb may be present. (a) Write an equation for the nuclear process. (b) Compare this technique with the conventional X-ray detection method.

Why is strontium-90 a particularly dangerous isotope for humans? The half-life of strontium-90 is 29.1 years. Calculate the radioactivity in millicuries of $15.6\mathrm{mg}$ of ${}^{90}\mathrm{Sr}$