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College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

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BuyFindarrow_forward

College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

Construct Your Own Problem

Consider 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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