Question

Archeologists can determine the age of artifacts made of wood or bone by measuring the amount of the radioactive isotope 14C present in the object. The amount of isotope decreases in a first-order process. If 15.5% of the original amount of 14C is present in a wooden tool at the time of analysis, what is the age of the tool? The half-life of 14C is 5730 yr.

Answer 1

Answer: The age of the tool is 15539 years

Explanation:

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 = $\frac{15.5}{100}\times 100=15.5$  

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.  

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

$k=\frac{0.693}{5730yr}=0.00012yr^{-1}$

b) for 15.5 % of original amount

$t=\frac{2.303}{0.00012}\log\frac{100}{15.5}$

$t=15539years$

Thus age of the tool is 15539 years