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Homework Help: Photon energy and momentum paradox

  1. Jan 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the momentum and energy of photons of light of wavelength 500nm. Usual data of h = 6.63 x 10-34 and c = 3.0 x 108ms-1

    2. Relevant equations

    3. The attempt at a solution
    > To get momentum, i simply take momentum = h/wavelength = 1.326 x 10-27 kgms-1

    > To get energy I use E = hf = 3.96 x 10-19 J

    > However, i figured that an alternative way to get energy will be to use the equation p = mv. Since i have already calculated the momentum of my photon in the first step, and I know that the velocity of a photon is 3.0 x 108 ms-1, the mass of the photon will be 4.42 x 10-36 kg. With this mass in mind, I can now use KE = 0.5mv2 (m = 4.42 x 10-36, v = 3.0 x 108 ms-1). Eventually, i obtain a KE of 1.99 x 10-19 J.

    > So there is now this paradox that E=hf gives me energy as 3.96 x 10-19 J, while the alternative method gives me energy of 1.99 x 10-19 J, which is half that of the former. Im pretty sure im missing out on something here. Any idea? Thanks!
  2. jcsd
  3. Jan 9, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    The equation p = mv only applies to particles moving slowly compared to light speed. It certainly doesn't apply to photons, which have m = 0.
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