Question #112602
2. In 40 days, the number of radioactive nuclei decreases to one-sixteenth the number present initially. What is the half-life (in days) of the material?
1
Expert's answer
2020-04-28T09:31:09-0400

The radioactive decay law says


N(t)=N02t/t1/2N(t)=N_02^{-t/t_{1/2}}

Hence, the half-life period

t1/2=tlog2(N/N0)=40log2(1/16)=10dayst_{1/2}=-\frac{t}{\log_2(N/N_0)}=-\frac{40}{\log_2(1/16)}=10\:\rm days

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