# 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.

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

97% (164 ratings) ###### 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?