Fundamentals of Physics Extended (10th Edition)

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

Chapter 43 - Energy from the Nucleus - Problems - Page 1332: 37b

Answer

$$3.1 \times 10^{-4}$$

Work Step by Step

We assume that rate of mass loss still (fixed or constant). Then, total mass loss will be: $\begin{aligned} \Delta M &=(d M / d t) \Delta t=\left(4.33 \times 10^{9} \mathrm{kg} / \mathrm{s}\right)\left(4.5 \times 10^{9} \mathrm{y}\right)\left(3.156 \times 10^{7} \mathrm{s} / \mathrm{y}\right) \\ &=6.15 \times 10^{26} \mathrm{kg} \end{aligned}$ The fraction lost is $$ \frac{\Delta M}{M+\Delta M}=\frac{6.15 \times 10^{26} \mathrm{kg}}{2.0 \times 10^{30} \mathrm{kg}+6.15 \times 10^{26} \mathrm{kg}}=3.1 \times 10^{-4} $$
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