Rock age of uranium and carbon

Question

Determine the age of a rock containing .065g of 238uranium(Half-life: 4.5x10^9) and .042 of 206Carbon. (Assume all lead came from U). Enter answer in scientific notation and with correct sig figs. 

Answer 1

I assume the final isotope is lead 206.   As an approximation, in this chain, the half lives of the intermediates are short compared to that of U238.   So we can assume that the total amount of Pb and U is the original amount of uranium in the sample.   

 

0.065 + 0.042 =   0.107 grams  

 

0.107 * (0.5)^t = 0.65 where t is the number of half lives.   we can solve for t

 

t = log_0.5 (0.065/.107) = .719   half lives.    So the total age is 0.719* 4.5* 10^9 = 3.2 * 10^9   (two significant figures since that is the best we know of the half life)

 

Based on the negative response, I worked the problem using a different formula from wikipedia

 

https://en.wikipedia.org/wiki/Uranium%E2%80%93lead_dating

 

N206/N238 = e^kt -1 where  k equal decay rate =  (ln 2)/4.5 * 10^9 = 1.54 * 10^-10.

 

(.042/0.065)  = exp(1.54*10^-10t) -1 

 

1.646  = exp(1.54*10^-10 * t)

ln 1.646 =  1.54*10^-10 * t

 

t = ln (1.646)/(1.54 * 10^-10) = 3.23 * 10^9.   But only two significant figures should be reported.  Notice that the answer is the same as the original answer.