Respuesta :
Answer:
The age of this archeological sample is 2737.53 years
Explanation:
Given that:
Half life = 5730 years
[tex]t_{1/2}=\frac {ln\ 2}{k}[/tex]
Where, k is rate constant
So,
[tex]k=\frac {ln\ 2}{t_{1/2}}[/tex]
[tex]k=\frac{\ln\ 2}{5730}\ year^{-1}[/tex]
The rate constant, k = 0.00012 year⁻¹
Using integrated rate law for first order kinetics as:
[tex][A_t]=[A_0]e^{-kt}[/tex]
Where,
[tex][A_t][/tex] is the concentration at time t
[tex][A_0][/tex] is the initial concentration
Given that:
The rate constant, k = [tex]0.00012[/tex] year⁻¹
It is given that 72 % of the 14C remains. So,
[tex]\frac {[A_t]}{[A_0]}[/tex] = 0.72
Applying values as:-
[tex]\frac {[A_t]}{[A_0]}=e^{-k\times t}[/tex]
[tex]0.72 =e^{-0.00012\times t}[/tex]
[tex]\ln \left(0.72\right)=-0.00012t\ln \left(e\right)[/tex]
[tex]\ln \left(0.72\right)=-0.00012t[/tex]
[tex]t=2737.53\ years[/tex]
The age of this archeological sample is 2737.53 years
