   Chapter 28, Problem 71PE

Chapter
Section
Textbook Problem

Construct Your Own ProblemConsider a highly relativistic particle. Discuss what is meant by the term "highly relativistic." (Note that, in part, it means that the particle cannot be massless.) Construct a problem in which you calculate the wavelength of such a particle and show that it is very nearly the same as the wavelength of a massless particle, such as a photon, with the same energy. Among the things to be considered are the rest energy of the particle (it should be a known particle) and its total energy, which should be large compared to its rest energy.

To determine

The term “highly relativistic.” And a problem to calculate the wavelength of such a particle and show that it is nearly the same as the wavelength of a mass less particle with the same energy.

Explanation

The relativistic particle has velocity nearly equal to the velocity of light.

Given info:

me=9.11×1031 kg

h=6.26×1034 Js1

v=0.9c

c=3×108 ms1

Formula used:

For total energy in of the relativistic particle, the relation between energy and velocity is

Eγmc2

Relativistic factor is

γ11 v 2 c 2

Total relativistic particle momentum is

pγmv

Wavelength of the particle

λhp

Wavelength due to relativistic energy

λhcE

Calculation:

Substituting the given values of energy in relation with velocity, we get

E1 1 v 2 c 2 mc2E1 1 (0.9c) 2 c 2 ×9.11×1031×(3×108)2E1

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