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Template:Infobox untriseptium Untriseptium (/ˌuːntraɪˈsɛptiəm/), also known as eka-dubnium or element 137, 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 imply that the periodic table ends soon after the island of stability at unbihexium. Its atomic number is 137 and symbol is Uts.

The name untriseptium is a temporary IUPAC systematic element name.

Significance

Untriseptium is sometimes called feynmanium (symbol Fy) because 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. However, a more rigorous analysis calculates the limit to be Z ≈ 173.

Bohr model breakdown

The Bohr model exhibits difficulty for atoms with atomic number greater than 137, for the speed of an electron in a 1s electron orbital, v, is given by

${\displaystyle v=Z\alpha c\approx {\frac {Zc}{137.036}}}$

where Z is the atomic number, and α is the fine structure constant, a measure of the strength of electromagnetic interactions. Under this approximation, any element with an atomic number of greater than 137 would require 1s electrons to be traveling faster than c, the speed of light. Hence the non-relativistic Bohr model is clearly inaccurate when applied to such an element.

The Dirac equation

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

${\displaystyle E=mc^{2}{\sqrt {1-Z^{2}\alpha ^{2}}}}$

where m is the rest mass of the electron. 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 including the effects of the finite size of the nucleus indicate that the binding energy first exceeds 2mc for Z > Z_cr ≈ 173. For Z > Z_cr, 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.

See also

• Dubnium
• Untrihexium – Untrioctium
• Atomic orbital, section Relativistic effects

References

1. Seaborg, G. T. (ca. 2006). "transuranium element (chemical element)". Encyclopædia Britannica. Retrieved 2010-03-16. {{cite web}}: Check date values in: |date= (help)
2. Cwiok, S.; Heenen, P.-H.; Nazarewicz, W. (2005). "Shape coexistence and triaxiality in the superheavy nuclei". Nature. 433 (7027): 705. Bibcode:2005Natur.433..705C. doi:10.1038/nature03336. PMID 15716943. {{cite journal}}: More than one of |pages= and |page= specified (help)
3. Elert, G. "Atomic Models". The Physics Hypertextbook. Retrieved 2009-10-09.
4. See Extended periodic table.
5. See for example Eisberg, R.; Resnick, R. (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles. Wiley.
6. Bjorken, J. D.; Drell, S. D. (1964). Relativistic Quantum Mechanics. McGraw-Hill.
7. Greiner, W.; Schramm, S. (2008). "American Journal of Physics". 76: 509. {{cite journal}}: Cite journal requires |journal= (help), and references therein.

v t e Extended periodic table
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ① H He ② Li Be B C N O F Ne ③ Na Mg Al Si P S Cl Ar ④ K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr ⑤ Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe ⑥ Cs Ba La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn ⑦ Fr Ra Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Rf Db Sg Bh Hs Mt Ds Rg Cn Nh Fl Mc Lv Ts Og ⑧ 119 120 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 ‍ ‍ 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142
s-block g-block f-block d-block p-block

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