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: 37

Answer

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Work Step by Step

$$ ^{238}_{92}U \rightarrow ^{234}_{90}Th+^{4}_{2}He $$ The kinetic energy is low enough so that classical physics is applicable, i.e., $KE=(p^2)/2m$. Calculate the thorium’s recoil KE. $$KE_{Th}=\frac{p_{Th}^2}{2m_{Th}}$$ Assuming the uranium nucleus is initially at rest, the two daughter nuclei have equal and opposite momentum. $$KE_{Th}=\frac{p_{\alpha}^2}{2m_{Th}}=\frac{2m_{\alpha}KE_{\alpha}}{2m_{Th}}$$ $$KE_{Th}=\frac{m_{\alpha} }{m_{Th}} KE_{\alpha}=\frac{4u}{234u}(4.20MeV)=0.0718MeV$$ The Q-value is the total kinetic energy of the thorium and of the alpha particle. Q=4.20 MeV+0.0718 MeV=4.27 MeV
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