# chem

posted by hannah

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 October 2005, when will it be necessary to replace the cobalt-60?

1. Steve

after t years, the fraction left is
2^(-t/5.26)

so, just solve
.75 = 2^(-t/5.26)
t = 2.183 years

2.183 years = 2 yrs + 2.2 months
so, it gets tossed in Dec 2007, or Jan 2008 (if it was purchased after Oct. 25)

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