Problem: 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?

FREE Expert Solution

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. 

lnNt = -kt + lnN0

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

t1/2=ln 2k

where: t1/2 = half-life


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Problem Details

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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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the First Order Half Life concept. You can view video lessons to learn First Order Half Life. Or if you need more First Order Half Life practice, you can also practice First Order Half Life practice problems.

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