Respuesta :
Answer: The age of the mineral sample is [tex]1.09\times 10^9yrs[/tex]
Explanation:
The equation used to calculate rate constant from given half life for first order kinetics:
[tex]t_{1/2}=\frac{0.693}{k}[/tex]
where,
[tex]t_{1/2}[/tex] = half life of the reaction = [tex]1.27\times 10^9yrs[/tex]
Putting values in above equation, we get:
[tex]k=\frac{0.693}{1.27\times 10^9yrs}=5.46\times 10^{-10}yrs^{-1}[/tex]
We are given:
Mass ratio of K-40 to Ar-40 = 0.812 : 1.00
Rate law expression for first order kinetics is given by the equation:
[tex]k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}[/tex]
where,
k = rate constant = [tex]5.46\times 10^{-10}yr^{-1}[/tex]
t = time taken for decay process = ? yr
[tex][A_o][/tex] = initial amount of the sample = [1.00 + 0.812] = 1.812 grams
[A] = amount left after decay process = 1.00 grams
Putting values in above equation, we get:
[tex]5.46\times 10^{-10}=\frac{2.303}{t}\log\frac{1.812}{1}\\\\t=1.09\times 10^9yrs[/tex]
Hence, the age of the mineral sample is [tex]1.09\times 10^9yrs[/tex]
