Respuesta :
Answer:
t = 49.20 years
Explanation:
Half life expression for first order kinetic is:
Half life = 12.3 years
[tex]t_{1/2}=\frac{\ln2}{k}[/tex]
Where, k is rate constant
So,
[tex]k=\frac{\ln2}{t_{1/2}}[/tex]
[tex]k=\frac{\ln2}{12.3}\ years^{-1}[/tex]
The rate constant, k = 0.05635 years⁻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:
[tex][A_t][/tex] is 6.25 % of [tex][A_0][/tex]. So,
[tex]\frac {[A_t]}{[A_0]}[/tex] = 0.0625
t = ?
[tex]\frac {[A_t]}{[A_0]}=e^{-k\times t}[/tex]
[tex]0.0625=e^{-0.05635\times t}[/tex]
t = 49.20 years
