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 - General Problems - Page 883: 76

Answer

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Work Step by Step

The needed energy to remove one neutron from $\rm ^4_2He$. So first we need to find the difference between the mass of $\rm ^4_2He$ and $\rm ^3_2He+n$. Thus, $$\Delta E=mc^2=(m_{^3_2He}-[m_{^4_2He}+m_n])c^2$$ Plugging from Appendix B; 4.002603 $$\Delta E=\left[ (4.002603\times 1.67\times 10^{-27})-(3.016029\times 1.67\times 10^{-27})-( 1.008665\times 1.67\times 10^{-27}) \right](3\times 10^8)^2$$ $$\Delta E_1=\color{red}{\bf 20.7517}\;\rm MeV$$ Now we need to repeat this process for $\rm ^{13}_6C$; $$\Delta E=mc^2=(m_{^{13}_6C}-[m_{^{12}_6C}+m_n])c^2$$ $$\Delta E_2=\left[ (13.003355\times 1.67\times 10^{-27})-(12.000000\times 1.67\times 10^{-27})-( 1.008665\times 1.67\times 10^{-27}) \right](3\times 10^8)^2$$ $$\Delta E_2=\color{red}{\bf 4.98808}\;\rm MeV$$ To find how much $E_2$ is greater than $E_1$; $$\dfrac{E_1}{E_2}=\dfrac{20.7517}{4.98808}=4.16$$ $$E_1=\color{red}{\bf4.16} E_2$$
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