Answer :
Answer: The amount of Iodine-131 remain after 39 days is 0.278 grams
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 = 8.04 days
Putting values in above equation, we get:
[tex]k=\frac{0.693}{8.04days}=0.0862days^{-1}[/tex]
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]0.0862days^{-1}[/tex]
t = time taken for decay process = 39 days
[tex][A_o][/tex] = initial amount of the sample = 8.0 grams
[A] = amount left after decay process = ?
Putting values in above equation, we get:
[tex]0.0862=\frac{2.303}{39}\log\frac{8.0}{[A]}[/tex]
[tex][A]=0.278g[/tex]
Hence, the amount of Iodine-131 remain after 39 days is 0.278 grams