Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 42 - Nuclear Physics - Exercises and Problems - Page 1275: 42

Answer

${\bf 216}\, \text{MeV}$ Note: This is a rough estimate based on the graph, so your solution may vary slightly from ours.

Work Step by Step

The goal is to estimate the total energy released when a nucleus with a mass number of 240 fissions into two nuclei with a mass number of 120 each. From the mentioned graph, the binding energy per nucleon for a nucleus with a mass number of 240 is about $ 7.6 \, \text{MeV} $. So, the total binding energy $ B_{240} $ of the entire nucleus with mass number 240 is $$ B_{240} = \text{Binding energy per nucleon} \times \text{Mass number} = (7.6 \, \text{MeV}) \times 240 $$ $$ B_{240} = \bf 1824 \, \rm {MeV} $$ For a nucleus with a mass number of 120, the binding energy per nucleon, as estimated from the graph, is about $ 8.5 \, \text{MeV} $. So, the total binding energy $ B_{120} $ for each nucleus with mass number 120 is: $$ B_{120} = \text{Binding energy per nucleon} \times \text{Mass number} $$ $$ B_{120} = (8.5 \, \text{MeV}) \times 120 $$ $$ B_{120} = \bf 1020 \, \rm {MeV} $$ When the nucleus with mass number 240 splits into two nuclei with mass number 120, the total energy released is given by $$ E_{\text{released}} =2B_{120}-B_{240}= 2(1020)-1824 $$ $$ E_{\text{released}} = \color{red}{\bf 216}\, \text{MeV} $$
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