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: 25

Answer

$ KE_{max}=0.782MeV$.

Work Step by Step

The decay described is $^{1}_{0}n\rightarrow\;^{1}_{1}p +\;^{0}_{-1}e+\overline{\nu}$. Calculate the energy release from the difference in the masses, using data from Appendix B. The mass of the emitted electron is accounted for by using the atomic mass of $^{1}_{1}H$ on the right hand side. $$E_{release}=\left( m(^{1}_{0}n)-m(^{1}_{1}H) \right)c^2$$ $$ =\left(1.008665u-1.007825u\right)c^2\left( \frac{931.49MeV/c^2}{u}\right)$$ $$ E_{release}=0.782MeV$$ If we assume that the proton and the neutrino have negligible KE, and assume zero mass for the neutrino, the energy release is the maximum kinetic energy of the electron. $$ KE_{max}=0.782MeV$$
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