Conceptual Physics (12th Edition)

Published by Addison-Wesley
ISBN 10: 0321909100
ISBN 13: 978-0-32190-910-7

Chapter 34 - Think and Solve: 34

Answer

The neutron gets about 80 percent of the kinetic energy, and the alpha particle gets 20 percent.

Work Step by Step

The neutron and the alpha particle fly apart with equal and opposite momenta. You may write kinetic energy in terms of the momentum. $$KE = \frac{1}{2}mv^{2} = \frac{(mv)^{2}}{2m} = \frac{p^{2}}{2m}$$ For particles with the same momentum, KE is inversely proportional to mass. The alpha particle has four times the mass of the neutron, and thus has one-fourth the kinetic energy. Alternate solution: the neutron has $\frac{1}{4}$ the mass of the alpha particle, and equal momentum, so it has four times the speed. Compare the KE directly. For the neutron: $$KE = \frac{1}{2}m(4v)^{2} = 8 mv^{2}$$ For the alpha particle: $$KE = \frac{1}{2}4m(v)^{2} = 2 mv^{2}$$ The kinetic energies are in the ratio of 4:1, or 80:20. The neutron gets about 80 percent of the kinetic energy, and the alpha particle gets 20 percent.
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