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.
[tex]t_{\frac{1}{2}}=\frac{0.693}{k}[/tex]
[tex]k=\frac{0.693}{5730years}=1.21\times 10^{-4}years^{-1}[/tex]
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
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
[tex]t=\frac{2.303}{1.21\times 10^{-4}}\log\frac{100}{25}[/tex]
[tex]t=11460years[/tex]
Thus we can conclude that these charcoal fragments are about 11460 years old.
