Answer: It will take 9.13 minutes for the sample.
Explanation:
Expression for rate law for first order kinetics is given by:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
where,
k = rate constant
t = age of sample
a = initial amount of the reactant = [tex]2.81\times 10^4[/tex]
a - x = amount left after decay process = [tex]3.52\times 10^3[/tex]
a) for completion of half life:
Half life is the amount of time taken by a radioactive material to decay to half of its original value.
[tex]t_{\frac{1}{2}}=\frac{0.693}{k}[/tex]
[tex]k=\frac{0.693}{3.05min}=0.227min^{-1}[/tex]
b) for activity to decrease from 2.81E4 Ci to 3.52E3 Ci:
[tex]t=\frac{2.303}{0.227}\log\frac{2.81\times 10^4}{3.52\times 10^3}[/tex]
[tex]t=9.13min[/tex]
Thus it will take 9.13 minutes for the sample.
[tex]t_{99.9}=40min[/tex]
The time after which 99.9% reactions gets completed is 40 minutes
