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Here I saw that if an element above atomic no 137 has to exist, it must have electron speed greater than speed of light. My question is , has this calculation been done keeping in mind Einstein's relativity? {I am just asking, I have not done this calculation.}

Klaus-Dieter Warzecha
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Qwerty
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    Electrons, under quantum mechanics, do not have 'speeds' in the Bohr sense. But, if you asking if relativistic quantum mechanics is possible, it most certainly is. – Jon Custer Dec 03 '15 at 21:43
  • The article you cite is bad, and those calculation couldn't be relativistic – Mithoron Dec 03 '15 at 22:07
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    Possible duplicate of The last element's atomic number – Mithoron Dec 03 '15 at 22:10
  • @Mithoron they could be relativistic: "Dirac showed that there are no stable electron orbits for more than 137 electrons" http://physics.info/atomic-models/ – DavePhD Dec 03 '15 at 22:19
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    Already for elements in the fifth (or even earlier?) period, calculations of the inner electronic structure make no sense at all if relativity is not taken into account. – Karl Dec 03 '15 at 22:20
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    @DavePhD Geez, he's talking about Bohr. With Dirac you'd have oscillating ground state not "exceeding c". and with more precise analysis you have problem at about 173, but of another kind https://en.wikipedia.org/wiki/Extended_periodic_table#Feynmanium_and_elements_above_the_atomic_number_137 – Mithoron Dec 03 '15 at 22:38
  • @Mithoron but the same number 137 (from the fine structure constant) is the limit for Dirac or Sommerfeld relativistic theory. You get imaginary numbers in the energy equation above 137. Other changes in the model beyond considering relativity are needed to avoid the 137 limit. – DavePhD Dec 03 '15 at 22:56

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Yes, the value 137 occurs even considering Einstein's theory of special relativity.

137 comes from considering Sommerfeld or Dirac relativistic theories, when the nucleus is modeled as a point.

See equation 1 of A new method for solving the Z > 137 problem and for determination of energy levels of hydrogen-like atoms

DavePhD
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