College Physics (7th Edition)

Published by Pearson
ISBN 10: 0-32160-183-1
ISBN 13: 978-0-32160-183-4

Chapter 29 - The Nucleus - Learning Path Questions and Exercises - Exercises - Page 998: 20


(a) (2) one-eighth. (b) $\frac{1}{16,777,216}$

Work Step by Step

a) Time elapsed=3 h=$\frac{3\,h}{1\,h}$half-lives$=3$ half lives. After 3 half-lives, the fraction of the sample left is equal to $\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=(\frac{1}{2})^{3}=\frac{1}{8}$ (b) Time elapsed= 1 day= 24 hours= $\frac{24\,h}{1\,h}$=24 half-lives. After 24 half-lives, the fraction of the sample left would be $(\frac{1}{2})^{24}=\frac{1}{2^{24}}=\frac{1}{16,777,216}$
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