College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Chapter 27.6, Problem 27.4QQ
To determine

If the wavelength of a particle increases or not as the momentum of the particle increases.

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Consider two particles X and Y that have the same energy. If the mass of particle X is 2000 times the mass of particle Y, which of the two particles has the largest wavelength and by how much?
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For a free relativistic quantum particle moving with speed u, the total energy of the particle is E = hf = hω = √p2c2 + m2c4 and the momentum is p = h/λ = hk = γmu. For the quantum wave representing the particle, the group speed is υg = dω/dk. Prove that the group speed of the wave is the same as the speed of the particle.
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