Question

A sample of cobalt-60 (t₁/₂= 5.27 yr), a powerful g emitter used to treat cancer, was purchased by a hospital on March 1, 2012. The sample must be replaced when its activity reaches 70.% of the original value. On what date must it be replaced?

Answer 1

The  sample of cobalt-60 (t₁/₂= 5.27 yr) must be replaced after 2.7 years which makes 2 years and 8.4 months. if the sample was purchased on march 2012 then it must be replaces on mid January 2015.

Briefly explained

To determine when the cobalt 60 needs to be replaced when it has achieved 70% of the activity. We simply need to use the first order integrated rate law which will allow us to calculate the time. However, when using this equation we need the Decay constant for Cobalt 60, which we can get from the half life of Cobalt 60.

We simply divide the half life of 5.27 years into the natural log of two and we get .13151 over years. If we have reached 70 Then 70% expressed as a decimal .7. So we have .7 of an original amount of one. So you can think of this as being divided by one. So the natural log of the amount at time T divided by the original amount is equal to negative K. Which we just calculated, multiplied by T.

With some algebraic rearrangement we get 2.7 years. So 2.7 years from the purchase of March one in 2012 is approximately early 2015.

Learn more about decay

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