Part A Answer two (2) Questions from Part A. Write your answers on the pages pro

Question

Part A Answer two (2) Questions from Part A. Write your answers on the pages provided at the end of the examination. Carbon 14 is a radioactive isotope produced in the upper atmosphere by cosmic rays. It has a half-life measured as 5730 + 40 years. Since plants and animals absorb carbon from the atmosphere, the percentage of carbon a living organism contains that is carbon 14 is equal to the percentage of carbon 14 in the atmosphere. When an organism dies, however (or when a layer of wood is laid down as bark in a tree), it ceases to a carbon. Since carbon 12 (the normal form of carbon) is stable, this means that the ratio of carbon 14 to carbon 12 in an organism decays exponentially after death of that organism. This is the basis of radio-carbon dating 1. bsorb Suppose that an element K is to be used for radioactive dating. K occurs in two isotopes, Ki and K2, with respective half-lives th and t2, with t2 > t. Assuming the ratio of Ki to K2 in the atmosphere is constant and corresponds to the ratio in living organisms, find the equation describing the decay of this ratio after an organism dies. (4 pts)

Explanation / Answer

For the radioisotope K1, let K1 = K1o *e -lambda1*t

For the radioisotope K2, let K2 = K2o *e -lambda2*t

For K1, at t = t1 (half-life), K1o/2 = K1o *e -lambda1*t1

=> lambda1 = -ln0.5/t1

Therefore, K1 = K1o *e (ln0.5/t1)*t ;

Similarly,  K2= K2o *e (ln0.5/t2)*t

Therefore, the ratio K1/K2 = (K1o * e(ln0.5/t1)*t)/ (K2o *e (ln0.5/t2)*t) = (K1/K2)o e ln0.5/t (1/t1 -1/t2)

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