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Element 129 superluminal? zαc

  1. Oct 31, 2013 #1
    I found the equation for the speed of an electron today. atomic number*fine-structure constant*speed of light. rearranging we get z= v/σc. if you set v to c then you find that at element 137 the electrons become superluminal. This can be possible right? a retrocausal atom! Could someone please explain why this wont happen. Thanks for any help.

    sorry, for the typo in the title.
    Last edited by a moderator: Oct 31, 2013
  2. jcsd
  3. Oct 31, 2013 #2
    This formula is a non-relativistic approximation, valid only for Z much smaller than 137. It is not true for large Z. (It is also a huge oversimplification that ignores things like the fact that different electrons in an atom have different velocities and the fact that that no electron has a definite velocity; nevertheless it does give the right order of magnitude for the electron velocity, as long as Z is much less than 137).
  4. Oct 31, 2013 #3
    what's the relativistic equation?
  5. Oct 31, 2013 #4


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    There's more involved than just "relativistic". For the nonrelativistic atom the energy of the ground state is

    E = - mc22 Z2/2)

    The corresponding relativistic formula (exact solution of the Dirac equation) is

    E = mc2 √(1 - α2Z2)

    For αZ << 1 it reduces to the rest mass mc2 plus the nonrelativistic value. However for αZ = 1 it goes to zero. This is a warning that the single-particle Dirac solution is no longer valid, since the negative energy solutions can no longer be ignored. In fact for αZ > 1 the energy becomes imaginary.
  6. Oct 31, 2013 #5
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