We are being asked the year it will be necessary to replace the cobalt-60 sample.
The sample has a half-life of 5.26 yrs.
Recall: Radioactive reactions follow principles dealing with Chemical Kinetics.
Radioactive decay follows a 1st order mechanism and so has a similar integrated rate law equation from Chemical Kinetics.
where: [N]t = final concentration
k = Decay constant in time-1
t = time
[N]0 = initial concentration
The decay constant can be calculated using the formula
where: t1/2 = half-life
Cobalt-60 is a strong gamma emitter that has a half-life of 5.26 yr. The cobalt-60 in a radiotherapy unit must be replaced when its radioactivity falls to 75% of the original sample.
If an original sample was purchased in June 2013, when will it be necessary to replace the cobalt-60?
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