Answer: The tree died 9709.46 years before.
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{30}{100}\times 100=30[/tex]
a) to find rate constant
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}{5600years}=1.24\times 10^{-4}years^{-1}[/tex]
b) to know the age
[tex]t=\frac{2.303}{1.24\times 10^{-4}}\log\frac{100}{30}[/tex]
[tex]t=9709.46years[/tex]
The tree died 9709.46 years before.
