## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

The half-life is $~~80~days$
We can write an expression for the decay rate: $r = \frac{ln~2}{t_{1/2}}$ We can find the half-life: $R = r~N$ $R = (\frac{ln~2}{t_{1/2}})~(N)$ $t_{1/2} = \frac{N~ln~2}{R}$ $t_{1/2} = \frac{(5.0\times 10^{15})~(ln~2)}{5.0\times 10^8}$ $t_{1/2} = 6.93147\times 10^6~s$ $t_{1/2} = (6.93147\times 10^6~s)[\frac{1~day}{(24)(3600~s)}]$ $t_{1/2} = 80~days$ The half-life is $~~80~days$