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The equation relating rate constant to half-life for first order kinetics is $k = \dfrac \label$ so the rate constant is then $k = \dfrac = 1.21 \times 10^ \text^ \label$ and Equation $$\ref$$ can be rewritten as $N_t= N_o e^ \label$ or $t = \left(\dfrac \right) t_ = 8267 \ln \dfrac = 19035 \log_ \dfrac \;\;\; (\text) \label$ The sample is assumed to have originally had the same (rate of decay) of d/min.g (where d = disintegration).
From the discovery of Carbon-14 to radiocarbon dating of fossils, we can see what an essential role Carbon has played and continues to play in our lives today.Once an organism is decoupled from these cycles (i.e., death), then the carbon-14 decays until essentially gone.The half-life of a radioactive isotope (usually denoted by $$t_$$) is a more familiar concept than $$k$$ for radioactivity, so although Equation $$\ref$$ is expressed in terms of $$k$$, it is more usual to quote the value of $$t_$$.This discovery is in contrast to the carbon dating results for the Turin Shroud that was supposed to have wrapped Jesus’ body.Carbon dating has shown that the cloth was made between 12 AD.