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

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 42 - Nuclear Physics - Exercises and Problems - Page 1236: 22

Answer

The half-life is $~~80~days$

Work Step by Step

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 $~~80~days$
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