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: 41

Answer

2.5 billion decays/second.

Work Step by Step

Calculate the activity using equation 30–3b. $$\frac{\Delta N}{\Delta t}=-\lambda N$$ We are interested in the number of counts per second, which is a positive number. Combine this with equation 30–6, which relates the decay constant to the half-life. $$\frac{\Delta N}{\Delta t}=\lambda N=\frac{ln 2}{T_{1/2}}N$$ The half-life for carbon-14, 5730 years, is found in Appendix B. $$|\frac{dN}{dt}|=\frac{ln 2}{(5730y)(3.16\times10^7s/y)}(6.5\times10^{20}\;nuclei)=2.5\times10^9$$
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