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: Q39.3

Answer

Yes. They are identical.

Work Step by Step

The de Broglie wavelength is given by $\lambda_{dB}=\frac{h}{p}$. For a photon, E=pc, so the photon has momentum $p=\frac{E}{c}$. Substituting, we see that $\lambda_{dB}=\frac{hc}{E}$. However, a photon’s energy is equal to hf, so we have $\lambda_{dB}=\frac{hc}{hf}=\frac{c}{f}=\lambda$. This is the wavelength of the associated electromagnetic wave.
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