Grothendieckium is the provisional non-systematic name of an undiscovered element with the symbol Gk and atomic number 194. Grothendieckium was named after Alexander Grothendieck (1928–2014), who made contributions to algebraic geometry. This hypothetical element with atomic number 194 is known in the scientific literature as unennquadium (Ueq) or simply element 194. It is located in the periodic table coordinate 6g20.
Atomic properties[]
Since its atomic number is greater than 173 (messierium), the properties below are only predicted. Its nucleus contains 194 protons and 381 neutrons, corresponding to its nuclear ratio (neutrons per proton) of 1.96. With reference to the elements before, it is quite certain that a grothendieckium atom has a mass greater than 570 amu. There are six electrons in the 7f orbital, four electrons in the 8d orbital and twelve electrons in the 6g orbital for this element.
Isotopes[]
Like every other element heavier than lead, grothendieckium has no stable isotopes. The longest-lived isotope is 575Gk. It should have a half life of at least 1 femtosecond and decay by spontaneous fission like other elements in this range.
It is also expected to have several isomers, which are excited states of normal ground state isotopes. It is possible that some of them have half-lives longer than the the longest-lived ground state isotope.
Chemical properties and compounds[]
Just as the lanthanides all have similar chemical properties while neptunium and plutonium share similarities with uranium, grothendieckium is expected to be like eddingtonium to riemannium in terms of chemical compounds. Therefore, grothendieckium is expected to form a +6 (hexavalent) oxidation state. In addition, it may exhibit lower oxidation states such as +4, losing electrons in the 8d orbital. Some possible compounds include hexafluorogrothendieckic acid (H2GkF6), tetraphenylgrothendieckium (Gk(C6H5)6) and other organogrothendieckium compounds.
Physical properties[]
Unusually for an element beyond period 7, grothendieckium has a color similar to that of iron, due to certain exchange of energies between different orbitals. These electrons excite energies at different regions of the visible spectrum in intensities similar to those in iron. Its density and molar volume has not been calculated yet. Like most metals, grothendieckium is predicted to be solid at room temperature and is predicted to be paramagnetic.
Occurrence[]
It is possible that grothendieckium doesn't exist in the universe at all, at any time in the past or in the future. This is because certain relativistic calculations state that the electrons of the 1s orbital will reach or exceed the speed of light in this element. Under this hypothesis, this element is impossible to create or exist. However, such a limit remains unproven, and it is possible that heavier elements and quantum mechanics will be further studied in the future, refining the limit of the number of protons an electrically neutral atom can have. Other common limits predicted include 137, 210 or even unlimited.
Synthesis[]
It might be impossible to synthesize grothendieckium due to quantum restrictions on the speed of electrons. If synthesis is possible, then nuclei of a couple lighter elements must be fused together, and the right amount of neutrons must be seeded. This operation would be impossible using current technology since it requires a tremendous amount of energy, thus its cross section would be so low that it is beyond the technological limit. Even if synthesis succeeds, this resulting element would almost immediately undergo fission.
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