Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 42 - Nuclear Physics - Questions - Page 1301: 3

Answer

There will be a time $t$ when $R_A = R_B$

Work Step by Step

We can write an expression for the decay rate: $R = R_0~e^{-\lambda t} = \frac{R_0}{e^{\lambda t}}$ The decay rate $R_A$ at $t=0$ is equal to the decay rate $R_B$ at $t = 30~min$ Then, initially, $R_B \gt R_A$ since a decay rate decreases over time. However, since $\lambda_B \gt \lambda_A$, as time increases, $R_B$ decreases more steeply than $R_A$. Therefore, there will be a time $t$ when $R_A = R_B$
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