Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 30 - Nuclear Physics and Radioactivity - General Problems - Page 884: 83

Answer

13 decays/s.

Work Step by Step

The fraction of atoms that are K-40 is very small. Use the atomic weight of K-39 to find the total number of K atoms in the sample. $$N_{K}=\frac{0.420g}{38.9637g/mol}(6.02\times10^{23}nuclei/mol)=6.49\times10^{21}$$ Now find the number of K-40 nuclei. $$N_{K-40}=0.000117(6.49\times10^{21})=7.59\times10^{17}$$ Calculate the activity using equation 30–3b. $$\frac{\Delta N}{\Delta t}=\lambda N=\frac{ln 2}{T_{1/2}}N$$ The half-life for K-40 is found in Appendix B. $$|\frac{dN}{dt}|=\frac{ln 2}{(1.248\times 10^9y)(3.156\times10^7s/y)}( 7.59\times10^{17}\;nuclei)$$ $$=13\;decays/s$$
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