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 883: 66

Answer

5.64 half-lives.

Work Step by Step

Use equations 30–5 for the activity. $$R=R_0e^{-\lambda t}$$ Now apply equation 30-6, and the given information that the current activity is 0.02 times the activity at the beginning. $$R=R_0e^{-(ln2)t/(T_{1/2})}=0.02R_0$$ $$0.02=e^{-(ln2)t/(T_{1/2})}$$ Solve for the ratio of the elapsed time to the half-life. $$\frac{t}{T_{1/2}}=-\frac{ln(0.02)}{ln 2}=5.64 $$ You must wait 5.64 half-lives.
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