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Problem 44 Medium Difficulty

Isotopes such as $^{26} \mathrm{Al}$ (half-life: $7.2 \times 10^{5}$ years) are believed to have been present in our solar system as it formed, but have since decayed and are now called extinct nuclides. .
(a) 26 Al decays by $\beta^{+}$ emission or electron capture. Write the equations for these two nuclear transformations.
(b) The earth was formed about $4.7 \times 10^{9}(4.7 \text { billion) years ago. How old was the earth when } 99.999999 \% \text { of the }$ 26 Al originally present had decayed?

Answer

a) $26 \mathrm{Al} \rightarrow_{12}^{26} \mathrm{Mg}+_{+1}^{0} \mathrm{e}$, $_{13}^{26} \mathrm{Al}+_{-1}^{0} \mathrm{e} \rightarrow_{12}^{26} \mathrm{Mg}$
b) $1.7 \times 10^{7}$ years

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