Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 39, Problem 30P

(a)

To determine

Show that (fc)2=1λ2+1λC2 for the moving quantum particle.

(b)

To determine

Whether it is possible for a particle of nonzero mass to have equal wavelength and frequency like a photon.

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A quantum particle of mass m is placed in a one-dimensional box of length L. Assume the box is so small that the particle’s motion is relativistic and K = p2/2m is not valid. (a) Derive an expression for the kinetic energy levels of theparticle. (b) Assume the particle is an electron in a box of length L = 1.00 × 10-12 m. Find its lowest possible kinetic energy. (c) By what percent is the nonrelativistic equation in error?
(a) Show that the frequency f and wavelength λ of a freely moving quantum particle with mass are related by the expression                                                             (F/c)2 = 1/λ2 + 1/λC2where λC = h/mc is the Compton wavelength of the particle. (b) Is it ever possible for a particle having nonzero mass to have the same wavelength and frequency as a photon? Explain.
(b) An electron confined in a one dimensional box emits a 200 nm photon in a quantum jump from n = 2 to n = 1. What is the length of the box? The mass of an electron is 9.11 x 1031 kg. (c) A proton confined in a one dimensional box emits a 2.0 MeV gamma-ray photon in a quantum jump from n = 2 to n = 1. What is the length of the box? The mass of a proton is 1.67 x 1027 kg.
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