Respuesta :
Answer: The half life of the given radioactive isotope is 43.86 minutes
Explanation:
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 = ?
t = time taken for decay process = 233 minutes
[tex][A_o][/tex] = initial amount of the reactant = 0.500 M
[A] = amount left after decay process = 0.0125 M
Putting values in above equation, we get:
[tex]k=\frac{2.303}{233}\log\frac{0.500}{0.0125}\\\\k=0.0158min^{-1}[/tex]
The equation used to calculate 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 = ?
k = rate constant = [tex]0.0158min^{-1}[/tex]
Putting values in above equation, we get:
[tex]t_{1/2}=\frac{0.693}{0.0158min^{-1}}=43.86min[/tex]
Hence, the half life of the given radioactive isotope is 43.86 minutes
