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I read that the mercury has a low melting point because its outer shell electrons are pulled in close by its nucleus (large nucleus, sparse outer shell) and because its outer shell electrons have significant relativistic mass. I think I remember them being roughly 1.28x the rest mass of an electron. I calculated that as meaning they must travel at roughly 60% of the speed of light. But are there faster electrons? (in orbitals, not just free electrons)

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This is the domain of relativistic quantum chemistry. This isn't something that has an easy upper bound, but you can imagine the 1-s orbital of ununoctium, if you'd like. On the extreme end you can imagine short-lived atoms in the vicinity of a magnetar

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My guess is that the OP could use a little more explanation. Why would the 1-s orbital of ununoctium be faster than 2-p of oxegen? Why magnetars? – Jess Riedel Nov 14 '13 at 1:43
The extreme magnetic fields make electrons in atoms behave ultra-relativistically. Regarding the first question, this is just a semi-classical guess (a la Bohr) but a 1-s orbital has greater speed than a 2-p orbital. Remember the Virial theorem $\langle T\rangle = -\frac{1}{2} \langle V \rangle$, or Kepler's laws if you like. – lionelbrits Nov 14 '13 at 10:52

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