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: 20

Answer

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Work Step by Step

Calculate the energy by finding the difference in the masses. a. Taking away a proton makes an isotope of carbon. Include the proton as a hydrogen atom, to balance the number of electrons. See Appendix B. $$E=\left( m(^{14}_{6}C)+m(^{1}_{1}H)-m(^{15}_{7}N)\right)c^2$$ $$ =\left( (14.003242u)+(1.007825u)-(15.000109u)\right)c^2\left( \frac{931.49MeV/c^2}{u}\right)$$ $$ =10.21MeV$$ b. Taking away a neutron makes an isotope of nitrogen. See Appendix B. $$E=\left( m(^{14}_{7}C)+m(^{1}_{0}n)-m(^{15}_{7}N)\right)c^2$$ $$ =\left( (14.003074u)+(1.008665u)-(15.000109u)\right)c^2\left( \frac{931.49MeV/c^2}{u}\right)$$ $$ =10.83MeV$$ The nucleons are held in the nucleus by the strong force. It is easier (takes less energy) to remove a proton because the other protons repel it.
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