# The mass of cobalt-60 in a sample is found to have decreased from 0.800g to 0.200g in a period of 10.5 years. From this information, what is the half-life of cobalt?

May 24, 2018

Let's assume radioactive decay follows first order kinetics.

Recall,

$\ln {\left[A\right]}_{\text{t}} = - k t + \ln {\left[A\right]}_{0}$

${t}_{\frac{1}{2}} = \ln \frac{2}{k}$

Let's derive the rate constant,

=> k = ln(([A]_"t")/([A]_0))/(-t) = 0.132"yr"^-1

Hence, the half life of cobalt-60 is,

${t}_{\frac{1}{2}} = \ln \frac{2}{k} \approx 5.25 \text{yr}$