Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 42 - Nuclear Physics - Problems - Page 1303: 24

Answer

$N_{\mathrm{Cu}} \Delta E_{\mathrm{be}}=1.6 \times 10^{25} \mathrm{MeV}$

Work Step by Step

The number of atoms in copper is \begin{align*} N_{\mathrm{Cu}}&=\left(\frac{3.0 \mathrm{g}}{62.92960 \mathrm{g} / \mathrm{mol}}\right)\left(6.02 \times 10^{23} \mathrm{atoms} / \mathrm{mol}\right)\\ & \approx 2.9 \times 10^{22} \text { atoms } \end{align*} The binding energy in the atom is \begin{aligned} \Delta E_{\mathrm{be}} &=(29(1.007825 \mathrm{u})+34(1.008665 \mathrm{u})-62.92960 \mathrm{u})(931.5 \mathrm{MeV} / \mathrm{u}) \\ &=551.4 \mathrm{MeV} \end{aligned} Hence, we get the total energy in the penny is $$N_{\mathrm{Cu}} \Delta E_{\mathrm{be}}=(551.4 \mathrm{MeV})\left(2.9 \times 10^{22}\right)=\boxed{1.6 \times 10^{25} \mathrm{MeV}}$$
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