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 881: 18

Answer

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Work Step by Step

a. See Example 30-4. $^{7}_{3}Li$ has 3 protons and 4 neutrons. Calculate the binding energy using the masses of the components and the mass of the nucleus. See Appendix B. $$E_{binding}=\left( 3m(^{1}_{1}H)+4m(^{1}_{0}n)-m(^{7}_{3}Li)\right)c^2$$ $$ =\left( 3(1.007825u)+4(1.008665u)-(7.016003u)\right)c^2\left( \frac{931.49MeV/c^2}{u}\right)$$ $$ =39.25MeV$$ Binding energy per nucleon is 39.2455MeV/7 nucleons = 5.607MeV/nucleon. b. See Example 30-4. $^{195}_{78}Pt$ has 78 protons and 117 neutrons. Calculate the binding energy using the masses of the components and the mass of the nucleus. See Appendix B. $$E_{binding}=\left( 78m(^{1}_{1}H)+117m(^{1}_{0}n)-m(^{195}_{78}Pt)\right)c^2$$ $$ =\left( 78(1.007825u)+117(1.008665u)-(194.964792u)\right)c^2\left( \frac{931.49MeV/c^2}{u}\right)$$ $$ =1546MeV$$ Binding energy per nucleon is 1545.68MeV/195 nucleons = 7.927MeV/nucleon.
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