# Use of isotopes in carbon dating

Climate science required the invention and mastery of many difficult techniques.These had pitfalls, which could lead to controversy.In a stratigraphical context objects closer to the surface are more recent in time relative to items deeper in the ground.Although relative dating can work well in certain areas, several problems arise.When it comes to dating archaeological samples, several timescale problems arise.

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).The man's body was recovered and pieces of tissue were studied for their C content by accelerator mass spectroscopy.The best estimate from this dating technique says the man lived between 33 BC. From the ratio, the time since the formation of the rock can be calculated.The technique of comparing the abundance ratio of a radioactive isotope to a reference isotope to determine the age of a material is called radioactive dating.Many isotopes have been studied, probing a wide range of time scales.