University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 39 - Particles Behaving as Waves - Problems - Discussion Questions - Page 1313: Q39.2

Answer

An electron has a longer de Broglie wavelength than a proton when they have the same kinetic energy.

Work Step by Step

The de Broglie wavelength is given by $\lambda=\frac{h}{p}$. If the electron and proton have the same kinetic energy KE, the smaller mass electron has the smaller momentum $p=\sqrt{(2)(m)(KE)}$. An electron has a longer de Broglie wavelength than a proton when they have the same kinetic energy.
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