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: 24

Answer

91.7%

Work Step by Step

Half-life of $\,\,^{131}I$=8.02 days Decay constant $\lambda=\frac{0.693}{t_{1/2}}=\frac{0.693}{8.02\,d}=0.086409\,d^{-1}$ $t=1\,d$ Recall that $\ln(\frac{A}{A_{0}})=-\lambda t$ where $A_{0}$ is the amount of sample at the beginning and $A$ is the amount sample after 1 day. $\implies \ln(\frac{A}{A_{0}})=-(0.086409\,d^{-1})(1\,d)=-0.086409$ Taking the inverse $\ln$ of both the sides, we have $\frac{A}{A_{0}}=e^{-0.086409}=0.917$ Percentage of the sample remaining=$0.917\times100\%=91.7\%$
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