Chapter 19: Problem 12
Describe the relative penetrating powers of alpha, beta, and gamma radiation.
Chapter 19: Problem 12
Describe the relative penetrating powers of alpha, beta, and gamma radiation.
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The first atomic explosion was detonated in the desert north of Alamogordo, New Mexico, on July \(16,1945 .\) What percentage of the strontium- 90\(\left(t_{1 / 2}=28.9 \text { years) originally produced }\right.\) by that explosion still remains as of July \(16,2017 ?\)
A rock contains 0.688 \(\mathrm{mg}^{206} \mathrm{Pb}\) for every 1.000 \(\mathrm{mg}^{238} \mathrm{U}\) present. Assuming that no lead was originally present, that all the \(^{206}\mathrm{P}\) formed over the years has remained in the rock, and that the number of nuclides in intermediate stages of decay between \(^{238} \mathrm{U}\) and \(^{206 \mathrm{P}} \mathrm{b}\) is negligible, calculate the age of the rock. (For $38 \mathrm{U}, t_{1 / 2}=4.5 \times 10^{9}$ years.)
The mass ratios of 40 \(\mathrm{Ar}\) to 40 \(\mathrm{K}\) also can be used to date geologic materials. Potassium-40 decays by two processes: $$_{19}^{40} \mathrm{K}+_{-1}^{0} \mathrm{e} \longrightarrow_{\mathrm{i} 8}^{40} \mathrm{Ar}(10.7 \%)$$ $$_{19}^{40} \mathrm{K} \longrightarrow_{20}^{40} \mathrm{Ca}+_{-1}^{0} \mathrm{e}(89.3 \%)$$ $$t_{1 / 2}=1.27 \times 10^{9}$$ a. Why are \(^{40}\mathrm{Ar} /^{40} \mathrm{K}\) ratios used to date materials rather than \(^{40}\mathrm{Ca} / 40 \mathrm{K}\) ratios? b. What assumptions must be made using this technique? c. A sedimentary rock has an Ar \(^{40} \mathrm{K}\) ratio of \(0.95 .\) Calculate the age of the rock. d. How will the measured age of a rock compare to the actual age if some \(^{40}\) Ar escaped from the sample?
Iodine- 131 is used in the diagnosis and treatment of thyroid disease and has a half-life of 8.0 days. If a patient with thyroid disease consumes a sample of \(\mathrm{Na}^{131} \mathrm{I}\) containing $10 . \mu \mathrm{g}^{131 \mathrm{I}}\( how long will it take for the amount of \)^{131} \mathrm{I}$ to decrease to 1\(/ 100\) of the original amount?
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