Answer: The time for organic matter has been reduced to 0.200% of its original value is 51400 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
t = age of sample
a = let initial amount of the reactant = 100
a - x = amount left after decay process = [tex]\frac{0.200}{100}\times 100=0.200[/tex]
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}{5730}=0.00012years^{-1}[/tex]
b) for reduction to 0.200% of its original value
[tex]t=\frac{2.303}{0.00012}\log\frac{100}{0.200}[/tex]
[tex]t=51400years[/tex]
The time for organic matter has been reduced to 0.200% of its original value is 51400 years
