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'''Untriseptium''' ({{pron-en|ˌuːntraɪˈsɛptiəm}}) is a hypothetical ] which has not been observed to occur naturally, nor has it yet been synthesised. Due to ], it is not known if this element is physically possible. Its atomic number is 137 and symbol is Uts.
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⚫ ]
The name ''untriseptium'' is a temporary ] ].

== Significance ==
Untriseptium is sometimes called '''feynmanium''' (symbol Fy) because ] noted<ref>
{{cite web
|author=G. Elert
|date=
|title=Atomic Models
|url=http://physics.info/atomic-models/
|work=The Physics Hypertextbook
|accessdate=2009-10-09
}}</ref> that a simplistic interpretation of the ] ] 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.<ref> See ].</ref>

=== Bohr model breakdown {{Anchor|Bohr model}} ===
The ] exhibits difficulty for atoms with atomic number greater than 137, for the speed of an electron in a ], ''v'', is given by

:<math>v = Z \alpha c \approx \frac{Z c}{137.036}</math>

where ''Z'' is the ], and ''α'' is the ], a measure of the strength of electromagnetic interactions.<ref>See for example {{cite book
|author=R. Eisberg, R. Resnick
|Year=1985
|title=Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles
|publisher=]
|isbn=
}}</ref> Under this approximation, any element with an atomic number of greater than 137 would require 1s electrons to be traveling faster than ''c'', the ]. Hence the non-relativistic Bohr model is clearly inaccurate when applied to such an element.

=== The Dirac equation ===
The ] ] also has problems for ''Z''&nbsp;>&nbsp;137, for the ground state energy is

:<math>E=m c^2 \sqrt{1-Z^2 \alpha^2}</math>

where ''m'' is the rest mass of the electron. For ''Z''&nbsp;>&nbsp;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 ].<ref>
{{cite book
|author=J.D. Bjorken, S.D. Drell
|year=1964
|title=Relativistic Quantum Mechanics
|publisher=]
|isbn=
}}</ref>

More accurate calculations including the effects of the finite size of the nucleus indicate that the binding energy first exceeds 2''mc''<sup>2</sup> for ''Z''&nbsp;>&nbsp;''Z''<sub>cr</sub>&nbsp;≈&nbsp;173. For ''Z''&nbsp;>&nbsp;''Z''<sub>cr</sub>, 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.<ref>
{{cite journal
|author=W. Greiner, S. Schramm
|year=2008
|title=]
|volume=76 |pages=509
|doi=
}}, and references therein.</ref>

More complete analysis involving relativity shows that the contradiction this particle poses may actually occur in the hypothetical element untriennium (''Z''&nbsp;=&nbsp;139; see ]).

==See also==
* ]
* ] &ndash; ]
* ], section ]

== References ==
{{Reflist}}

⚫ ]
]

]
]
]
]
]

Latest revision as of 04:14, 2 February 2023

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