Answer: The time taken by Cerium-143 will be 132.051 hours.
Explanation:
All the decay processes follow first order kinetics.
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 = 33 hours
k = ?
Putting values in above equation, we get:
[tex]k=\frac{0.693}{33hrs}=0.021hrs^{-1}[/tex]
Rate law expression for first order kinetics is given by the equation:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
where,
k = rate constant = [tex]0.021hrs^{-1}[/tex]
t = time taken for decay process = ? hours
a = initial amount of the reactant = 100 grams
a - x = amount left after decay process = 6.25 grams
Putting values in above equation, we get:
[tex]t=\frac{2.303}{0.021hrs^{-1}}\log\frac{100g}{6.25g}\\\\t=132.051hours[/tex]
Hence, the time taken by Cerium-143 will be 132.051 hours.
