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Minimum energy of an electron trapped in a nucleus

  1. Nov 12, 2011 #1
    We were asked to estimate the minimum kinetic energy of an electron trapped within a nucleus having diameter [tex] d [/tex].

    My solution was this: find the momentum of the electron (via de Broglie relation) and use a very standard kinetic energy formula, like this (assuming minimum energy state has a wavelength of twice the nucleus' diameter):

    [tex] p=h/\lambda=h/2d [/tex]
    [tex] E_K = p^2/2m_e = \frac{h^2}{8d^2m_e} [/tex]

    The professors marked this as incorrect, and instead gave this solution ([tex] E_0 [/tex] is electron rest mass, 0.511 MeV):

    [tex] p=h/\lambda=h/2d [/tex]
    [tex] E_K = [(pc)^2 + E_0^2]^{1/2} - E_o [/tex]

    These give drastically different results, but I'm just curious why the professor's approximation is physically more valid than my own.
     
  2. jcsd
  3. Nov 12, 2011 #2

    ehild

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    You need to use relativistic equations when the speed of electron is comparable with c.

    ehild
     
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