Problem: The half-life of cesium-130 is 15 minutes. What percentage of the initial activity will be present after 75 minutes, assuming radioactive decay occurs by a first order rate mechanism?a. 0.312%b. 70.71%c. 4.25%d. 1.14%e. 3.13% 

FREE Expert Solution

We’re being asked to determine the percentage of the initial activity of cesium-130 will be present after 75 minutes, assuming radioactive decay occurs by a first-order rate mechanism.


Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:


ln [N]t=-kt+ln [N]0


where:

[N]t = concentration at time t

k = decay constant

t = time

[N]0 = initial concentration


Also, recall that half-life is the time needed for the amount of a reactant to decrease by 50% or one-half


The half-life of a first-order reaction is given by:


t12=ln 2k


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Problem Details

The half-life of cesium-130 is 15 minutes. What percentage of the initial activity will be present after 75 minutes, assuming radioactive decay occurs by a first order rate mechanism?

a. 0.312%
b. 70.71%
c. 4.25%
d. 1.14%
e. 3.13%