Answer to Question #166473 in Atomic and Nuclear Physics for lauren

Question

a sample of cobalt-60 whose original activity is 64 Bq, how long would it take to decay to activity of 1Bq

Answer 1

Let’s use the formula for radioactive decay:

$$A=A_0e^{-\lambda t},$$ $$\dfrac{A}{A_0}=e^{-\lambda t},$$ $$ln(\dfrac{A}{A_0})=ln(e^{-\lambda t}),$$ $$ln(\dfrac{A}{A_0})=-\dfrac{0.693}{T_{1/2}}t,$$ $$t=-\dfrac{ln(\dfrac{A}{A_0})}{0.693}T_{1/2}=-\dfrac{ln(\dfrac{1\ Bq}{64\ Bq})}{0.693}\cdot5.27\ yr=31.6\ yr.$$