Question

You are an archaeologist who has just found an ancient fire ring containing charcoal fragments. You send these fragments to the lab for Carbon-14 analysis. The report you receive from the lab states that these fragments have 25% of the amount of Carbon-14 compared to modern wood. Using 5730 years as the half-life of Carbon-14, you conclude that these charcoal fragments are about ________ years old. Can you explain how you get an answer of 11460? Thank you!

Answer 1

Answer:Thus we can conclude that these charcoal fragments are about 11460 years old.

Explanation:

a) for completion of half life:  

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

$t_{\frac{1}{2}}=\frac{0.693}{k}$

$k=\frac{0.693}{5730years}=1.21\times 10^{-4}years^{-1}$

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant  

t = age of sample

a = let initial amount of the reactant  = 100

a - x = amount left after decay process = 25

b) for completion of 75 % of reaction  

$t=\frac{2.303}{1.21\times 10^{-4}}\log\frac{100}{25}$

$t=11460years$

Thus we can conclude that these charcoal fragments are about 11460 years old.