Answer: The amount of sample left after 8323 years is 4.32g
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
a - x = amount left after decay process
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}{8694years}=7.97\times 10^{-5}years^{-1}[/tex]
b) amount left after 8323 years
[tex]t=\frac{2.303}{7.97\times 10^{-5}}\log\frac{8.30g}{a-x}[/tex]
[tex]8323=\frac{2.303}{7.97\times 10^{-5}}\log\frac{8.30g}{a-x}[/tex]
[tex]0.285=\log\frac{8.30}{a-x}[/tex]
[tex]\frac{8.30}{a-x}=1.92[/tex]
[tex](a-x)=4.32g[/tex]
The amount of sample left after 8323 years is 4.32g
