Respuesta :
Answer:
2578.99 years
Explanation:
Given that:
100 g of the wood is emitting 1120 β-particles per minute
Also,
1 g of the wood is emitting 11.20 β-particles per minute
Given, Decay rate = 15.3 % per minute per gram
So,
Concentration left can be calculated as:-
C left = [tex][A_t]=\frac{11.20\ per\ minute}{15.3\ per\ minute\ per\ gram}\times [A_0]= 0.7320[A_0][/tex]
Where,
[tex][A_t][/tex] is the concentration at time t
[tex][A_0][/tex] is the initial concentration
Also, Half life of carbon-14 = 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}\ years^{-1}[/tex]
The rate constant, k = 0.000120968 year⁻¹
Time =?
Using integrated rate law for first order kinetics as:
[tex][A_t]=[A_0]e^{-kt}[/tex]
So,
[tex]\frac {[A_t]}{[A_0]}=e^{-0.000120968\times t}[/tex]
[tex]\frac {0.7320[A_0]}{[A_0]}=e^{-0.000120968\times t}[/tex]
[tex]0.7320=e^{-0.000120968\times t}[/tex]
[tex]ln\ 0.7320=-0.000120968\times t[/tex]
t = 2578.99 years
