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Homework Help: DeBroglie wavelength and nucleon velocity

  1. Aug 29, 2011 #1
    1. The problem statement, all variables and given/known data

    Atomic nucleus consists of nucleons. What velocity (order of magnitude estimate) will a nucleon have inside a nucleus?

    2. Relevant equations

    [itex]\lambda[/itex] = h/mv

    v = h/m[itex]\lambda[/itex]

    3. The attempt at a solution

    The wavelength of a nucleus is on the order of 10^-15/m, nucleons have a mass on the order of 10^-27 kg, and h is Plancks Constant. If I do a straight plung-n-chug I get that the velocity should be on the order of 10^-22 m/s.

    It seems reasonable to me, but recently that's been a guarantee that it isn't. So does that look reasonable to anyone else?
  2. jcsd
  3. Aug 29, 2011 #2


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    No, that's not correct. A length scale of 1 fm corresponds to an energy of 197 MeV, which is a good chunk of the 1 GeV mass of a nucleon. You should expect the nucleon to be moving relativistically.
  4. Aug 29, 2011 #3
    Ok, ran it again this time assuming a wavelength for the nucleus of ~10^-14m (a big-ish nucleus), and a nucleon mass of 1GeV/c^2 and came up with a velocity of ~0.4c. Which makes considerably more sense than my first answer.
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