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 1 ^{st} order mechanism**

$\overline{){\mathbf{ln}}{\left[\mathbf{N}\right]}_{{\mathbf{t}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{ln}}{\left[\mathbf{N}\right]}_{{\mathbf{0}}}}$

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

$\overline{){{\mathbf{t}}}_{\mathbf{1}\mathbf{/}\mathbf{2}}{\mathbf{=}}\frac{\mathbf{ln}\mathbf{}\mathbf{2}}{\mathbf{k}}}$

where: *t _{1/2} = 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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