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(A) The decay of carbon follows first-order kinetics. Given: Initial activity $(r_o)$ = $15.2 \ min^{-1} g^{-1}$,Final activity $(r)$ = $7.6 \ min^{-1

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$5760$ years

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(A) The decay of carbon follows first-order kinetics. Given: Initial activity $(r_o)$ = $15.2 \ min^{-1} g^{-1}$,Final activity $(r)$ = $7.6 \ min^{-1} g^{-1}$,and $t_{1/2} = 5760$ years. Since $r = \frac{r_o}{2}$,the artifact has undergone exactly one half-life. Therefore,the age of the artifact $(t)$ = $1 	imes t_{1/2} = 5760$ years. Alternatively,using the formula $t = \frac{t_{1/2}}{0.693} \ln(\frac{r_o}{r}) = \frac{5760}{0.693} \ln(\frac{15.2}{7.6}) = \frac{5760}{0.693} \ln(2) = 5760$ years.

$A$ wooden artifact and a freshly cut tree have carbon activity of $7.6$ and $15.2 \ min^{-1} g^{-1}$ respectively. Given the half-life $(t_{1/2})$ of carbon is $5760$ years,the age of the artifact is:

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