Answer:
20619.4793 years
Explanation:
The half life of carbon-14 = 5730 years
The formula for the half life for a first order kinetic reaction is:
[tex]t_{1/2}=\frac {ln\ 2}{k}[/tex]
Where,
[tex]t_{1/2}[/tex] is the half life
k is the rate constant.
Thus rate constant is:
5730 years=ln(2)/k
k = 1.21×10⁻⁴ years ⁻¹
Using integrated rate law as:
[tex]ln\ \frac {A_t}{A_0}=-k\times t[/tex]
Where,
[tex]A_t[/tex] is the concentration at time t
[tex]A_0[/tex] is the initial concentration
Given that the final concentration contains 8.25 % of the original quantity which means that:
[tex]\frac {A_t}{A_0}=0.0825[/tex]
So,
ln(.0825)= -1.21×10⁻⁴×t
t = 20619.4793 years
