Chapter 19: Problem 9
Why are the observed energy changes for nuclear processes so much larger than the energy changes for chemical and physical processes?
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Chapter 19: Problem 9
Why are the observed energy changes for nuclear processes so much larger than the energy changes for chemical and physical processes?
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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?
Predict whether each of the following nuclides is stable or unstable (radioactive). If the nuclide is unstable, predict the type of radioactivity you would expect it to exhibit. a. \(_{19}^{45} \mathrm{K}\) b. \(_{56}^{26} \mathrm{Fe}\) c. \(_{20}^{11} \mathrm{Na}\) d. \(_{194}^{81} \mathrm{TI}\)
Photosynthesis in plants can be represented by the following overall equation: $$ 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \stackrel{\mathrm{} Light \mathrm{}}{\longrightarrow} C_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) $$ Algae grown in water containing some \(^{18} \mathrm{O}\left(\text { in } \mathrm{H}_{2}^{18} \mathrm{O}\right)\) evolve oxygen gas with the same isotopic composition as the oxygen bin the water. When algae growing in water containing only \(^{18} \mathrm{O}\) were furnished carbon dioxide containing \(^{18} \mathrm{O}\) no \(^{18} \mathrm{O}\) was found to be evolved from the oxygen gas produced. What conclusions about photosynthesis can be drawn from these experiments?
In addition to the process described in the text, a second process called the carbon-nitrogen cycle occurs in the sun: a. What is the catalyst in this process? b. What nucleons are intermediates? c. How much energy is released per mole of hydrogen nuclei in the overall reaction? (The atomic masses of \(_{1}^{1} \mathrm{H}\) and \(\frac{4}{2} \mathrm{He}\) are 1.00782 \(\mathrm{u}\) and \(4.00260 \mathrm{u},\) respectively.)
A recent study concluded that any amount of radiation exposure can cause biological damage. Explain the differences between the two models of radiation damage, the linear model and the threshold model.
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