User:Kepler-1229b/sandbox/Ust

Unsepttrium, also known as eka-unbitrium, dvi-protactinium, or element 173, is a hypothetical chemical element which has not been observed to occur naturally, nor has it yet been synthesised. Due to drip instabilities, it is not known if this element is physically possible, as the drip instabilities may imply that the periodic table ends soon after the island of stability at unbihexium; however, if possible, it is likely the heaviest possible neutral element. Its atomic number is 173 and its atomic symbol is Ust.

The name unsepttrium is a temporary IUPAC systematic element name.

Significance
Although Richard Feynman noted that a simplistic interpretation of the relativistic Dirac equation runs into problems with electron orbitals at Z > 1/α = 137, suggesting that neutral atoms cannot exist beyond untriseptium, and that a periodic table of elements based on electron orbitals therefore breaks down at this point, a more rigorous analysis calculates the limit to be Z ≈ 173, meaning that neutral atoms most likely cannot exist with Z greater than 173. This makes unsepttrium theoretically the heaviest neutral element possible.

The Dirac equation
The relativistic Dirac equation has problems for Z > 137, for the ground state energy is


 * $$E=m c^2 \sqrt{1-Z^2 \alpha^2}$$

where m is the rest mass of the electron. Although for Z > 137, the wave function of the Dirac ground state is oscillatory, rather than bound, and there is no gap between the positive and negative energy spectra, as in the Klein paradox, more accurate calculations taking into account the effects of the finite size of the nucleus indicate that the binding energy first exceeds 2mc2 for Z > Zcr ≈ 173. For Z > Zcr, if the innermost orbital is not filled, the electric field of the nucleus will pull an electron out of the vacuum, resulting in the spontaneous emission of a positron.