Please help

Question

a. The ratio of carbon 14 to carbon 12 in a piece of wood discovered in a cave is
R = 1/814.
Estimate the age of the piece of wood. (Round your answer to the nearest whole number.)

 

b. The ratio of carbon 14 to carbon 12 in a piece of paper buried in a tomb is
R = 1/1311.
Estimate the age of the piece of paper. (Round your answer to the nearest whole number.)

Answer 1

the formula for the dating process is t = [ log_n R / -0.693 ] • 5730 where log_n = the natural logarithm, -0.693 = decay rate, and 5730 = half life in years

 

using your values, t = [ log_n (1/814) / -0.693 ] • 5730y = 55,400 years

assuming the sample was uncontaminated, the result will be beyond the recognized limit for radio carbon dating

 

regarding sample 2, there are two considerations

first, the calculation will result in a value well beyond the recognized limit of radio carbon dating

second, if the date is correct, then something else is wrong because paper was unknown at that time in history

 

Please see http://mathcentral.uregina.ca/beyond/articles/ExpDecay/Carbon14.html

for a detailed explanation