Modern Physics
Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 6, Problem 14P

(a)

To determine

The expression for energy levels of particle using relativistic energy-momentum relation and quantization of momentum.

(b)

To determine

The lowest possible kinetic energy; comparison with non-relativistic energy of particle.

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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?
In an experiment, a light source of 620 nm is used to eject electrons from a material. Initially, there is emission. The emission takes place when the material is moved towards the material at a velocity of 0.3c. From this data calculate the work function of the material.
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