Answer: The age of the tool is 15539 years
Explanation:
Expression for rate law for first order kinetics is given by:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
where,
k = rate constant Â
t = age of sample
a = let initial amount of the reactant = 100
a - x = amount left after decay process = [tex]\frac{15.5}{100}\times 100=15.5[/tex] Â
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. Â
[tex]t_{\frac{1}{2}}=\frac{0.693}{k}[/tex]
[tex]k=\frac{0.693}{5730yr}=0.00012yr^{-1}[/tex]
b) for 15.5 % of original amount
[tex]t=\frac{2.303}{0.00012}\log\frac{100}{15.5}[/tex]
[tex]t=15539years[/tex]
Thus age of the tool is 15539 years
