# How to solve radiometric dating questions

The currently accepted value for the half-life of will remain; a quarter will remain after 11,460 years; an eighth after 17,190 years; and so on.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).After the passage of two half-lives only 0.25 gram will remain, and after 3 half lives only 0.125 will remain etc.To see how we actually use this information to date rocks, consider the following: Usually, we know the amount, N, of an isotope present today, and the amount of a daughter element produced by decay, D*.Using this hypothesis, the initial half-life he determined was 5568 give or take 30 years.The accuracy of this proposal was proven by dating a piece of wood from an Ancient Egyptian barge, of whose age was already known.

Throughout the years measurement tools have become more technologically advanced allowing researchers to be more precise and we now use what is known as the Cambridge half-life of 5730 /- 40 years for Carbon-14.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.The half-life is the amount of time it takes for one half of the initial amount of the parent, radioactive isotope, to decay to the daughter isotope.Thus, if we start out with 1 gram of the parent isotope, after the passage of 1 half-life there will be 0.5 gram of the parent isotope left.

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