March 30, 2017

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The kinetic energy of a massive particle is equal to the energy of a photon.  The massive particle moves at 1.49 % the speed of light.  
What is the ratio of the photon wavelength to the de Broglie wavelength of the particle?  (Assume the standard nonrelativistic expressions for the momentum and kinetic energy of the massive particle.)

  • Physics - ,

    The deBroglie wavelength of a particle is ë=h/mv
    The wavelength of a photon is ë=hc/E

    Since we know that the energy 'E' of the photon is equal to the Kinetic energy of the massive particle, E=1/2mv^2.
    We are also given that v is 0.0149c.

    This is the ratio

    hc/(1/2m(0.0149c)^2) : h/m(0.0149c)

    The equivalent terms on each side of the ratio cancel, leaving...

    2/(0.0149) : 1

    Your answer should be 134.23

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