use the half-life information to complete each table. (The formula $\mathcal{N}=\mathcal{N}_{0} e^{k t}$ is not required.) (a) Uranium- 228: half-life $=550$ sec (b) Uranium-238: half-life $=4.9 \times 10^{9}$ years
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Use the half-life information to complete each table. (The formula $\mathcal{N}=\mathcal{N}_{0} e^{k t}$ is not required.) (a) Uranium-228: half-life $=550$ seconds$$\begin{array}{llllll}t \text { (seconds) } & 0 & 550 & 1100 & 1650 & 2200 \\\mathcal{N} \text { (grams) } & 8 & & & \\\hline\end{array}$$ (b) Uranium-238: half-life $=4.9 \times 10^{9}$ years$$\begin{array}{lcccccc}\hline \multirow{2}{*}\begin{array}{l}\text { t (years) } \\\mathcal{N} \text { (grams) }\end{array} & \multicolumn{2}{c}0 \\& \multicolumn{2}{c}10 & 5 & 2.5 & 1.25 & 0.625 \\\hline\end{array}$$
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Use the half-life information to complete each table. (The formula $\mathcal{N}=\mathcal{N}_{0} e^{k t}$ is not required.) (a) Polonium-210: half-life $=138.4$ days $$\begin{array}{lllll}\hline t \text { (years) } & 0 & 138.4 & 276.8 & 415.2 \\\mathcal{N} \text { (grams) } & 0.4 & & & 0.025 \\\hline\end{array}$$ (b) Polonium-214: half-life $=1.63 \times 10^{-4}$ second $$\begin{array}{lllll}\hline t \text { (seconds) } & 0 & & & 6.52 \times 10^{-4} \\\mathcal{N} \text { (grams) } & 0.1 & 0.05 & 0.025 & 0.0125 & \\\hline\end{array}$$
The common isotope of uranium, $^{238} \mathrm{U},$ has a half-life of $4.47 \times 10^{9}$ years, decaying to $^{234} \mathrm{Th}$ by alpha emission. (a) What is the decay constant? (b) What mass of uranium is required for an activity of 1.00 curie? (c) How many alpha particles are emitted per second by 10.0 g of uranium?
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