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

Question #166473
a sample of cobalt-60 whose original activity is 64 Bq, how long would it take to decay to activity of 1Bq
1
Expert's answer
2021-02-25T11:26:23-0500

Let’s use the formula for radioactive decay:


A=A0eλt,A=A_0e^{-\lambda t},AA0=eλt,\dfrac{A}{A_0}=e^{-\lambda t},ln(AA0)=ln(eλt),ln(\dfrac{A}{A_0})=ln(e^{-\lambda t}),ln(AA0)=0.693T1/2t,ln(\dfrac{A}{A_0})=-\dfrac{0.693}{T_{1/2}}t,t=ln(AA0)0.693T1/2=ln(1 Bq64 Bq)0.6935.27 yr=31.6 yr.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.

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