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 - Problems - Page 882: 44

Answer

$N=8.5\times10^{19}\;nuclei$.

Work Step by Step

Calculate the activity using equation 30–3b. $$|\frac{\Delta N}{\Delta t}|=\lambda N$$ Combine this with equation 30–6, which relates the decay constant to the half-life. $$|\frac{\Delta N}{\Delta t}|=\frac{ln 2}{T_{1/2}}N$$ Solve for the number of nuclei. $$N=|\frac{\Delta N}{\Delta t}|\frac{T_{1/2}}{ln 2}$$ The half-life for U-238 is found in Appendix B. $$N=(420\;decays/s)\frac{(4.468\times10^9y)(3.156\times10^7s/y)}{ln 2}$$ $$N=8.5\times10^{19}\;nuclei$$
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