Physics Technology Update (4th Edition)

Published by Pearson
ISBN 10: 0-32190-308-0
ISBN 13: 978-0-32190-308-2

Chapter 32 - Nuclear Physics and Nuclear Radiation - Problems and Conceptual Exercises - Page 1153: 49

Answer

$^{1}_{0}n+^{235}_{92}U\rightarrow ^{88}_{38}Sr+^{136}_{54}Xe+12^{1}_{0}n;126.5MeV$

Work Step by Step

Firs of all, we complete the given reaction as follows: Number of neutrons in $^{235}_{92}U=235-92=143$ Number of neutrons in $^{88}_{38}Sr=88-38=50$ Number of neutrons in $^{136}_{54}Xe=136-54=82$ The number of neutrons in the system before reaction $143+1=144$ and the number of neutrons in the system after reaction $50+82+x=132+x$ We know that $144=132+x$ $\implies x=12$ Thus, the required reaction is $^{1}_{0}n+^{235}_{92}U\rightarrow ^{88}_{38}Sr+^{136}_{54}Xe+12^{1}_{0}n$ Now $\Delta m=m_f-m_i$ $\implies \Delta m=235.916825u-236.05259u=-0.135765u$ The required energy can be calculated as $E=|\Delta m|c^2$ We plug in the known values to obtain: $E=|-(0.135765u)(\frac{931.494\frac{MeV}{c^2}}{1u})|c^2$ $E=126.5MeV$
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