Nuclear decay is a first-order kinetics process. What is the half-life of a radioactive isotope if it takes 233 minutes for the concentration of the isotope to drop from 0.500 M to 0.0125 M? Give your answer in minutes.

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:

where,

k = rate constant  = ?

t = time taken for decay process = 233 minutes

= initial amount of the reactant = 0.500 M

[A] = amount left after decay process =  0.0125 M

Putting values in above equation, we get:

The equation used to calculate half life for first order kinetics:

where,

= half-life of the reaction = ?

k = rate constant =

Putting values in above equation, we get:

Hence, the half life of the given radioactive isotope is 43.86 minutes

the answer would be c