The method of carbon dating makes use of the fact that all living organisms cont
ID: 2842313 • Letter: T
Question
The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon-12, denoted 12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope). The ratio of the amount of 14C to the amount of 12C is essentially constant (approximately 1/10,000). When an organism dies, the amount of 12C present remains unchanged, but the 14C decays at a rate proportional to the amount present with a half-life of approximately 5700 years. This change in the amount of 14C relative to the amount of 12C makes it possible to estimate the time at which the organism lived.
(a) (4 points) A fossil found in an archaeological dig was found to contain 20% of the original amount of 14C. What is the approximate age of the fossil?
(b) (4 points) The Dead Sea Scrolls are approximately 2000 years old. What percent of the original 14C remains in them?
Explanation / Answer
or part A : use the formula: (1/2)^(t/5700) = 0.2
as we know, C-14's half life is 5700, if 1/2 of c-14 remains after 5700. After how many years (t) would only 20% (can be written as 1/5 in fraction) would remain?
it would be :
(1/2)^(t/5700)= (1/5)
take reciprocal on both sides:
2^(t/5700) = (5)
divide both sides by 2 and take log of both sides:
t/5700 = log2(5)
to simplify more:
t= 5700 log 2(5)
do the calculation and that would be your answer
b) For finding the % of C-14 (in decimal form) use the formula: C=(1/2)^(2000/5700)
Basically you are trying to figure out that if 1/2 of C-14 remains in 5700 years (half life of C-14), how much would remain in 2000 years, hence dividing the 2000 by 5700.
you'll get a value in decimal, which you have to then convert to percent.