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Extended periodic table

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Extended periodic table
Hydrogen Helium
Lithium Beryllium Boron Carbon Nitrogen Oxygen Fluorine Neon
Sodium Magnesium Aluminium Silicon Phosphorus Sulfur Chlorine Argon
Potassium Calcium Scandium Titanium Vanadium Chromium Manganese Iron Cobalt Nickel Copper Zinc Gallium Germanium Arsenic Selenium Bromine Krypton
Rubidium Strontium Yttrium Zirconium Niobium Molybdenum Technetium Ruthenium Rhodium Palladium Silver Cadmium Indium Tin Antimony Tellurium Iodine Xenon
Caesium Barium Lanthanum Cerium Praseodymium Neodymium Promethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutetium Hafnium Tantalum Tungsten Rhenium Osmium Iridium Platinum Gold Mercury (element) Thallium Lead Bismuth Polonium Astatine Radon
Francium Radium Actinium Thorium Protactinium Uranium Neptunium Plutonium Americium Curium Berkelium Californium Einsteinium Fermium Mendelevium Nobelium Lawrencium Rutherfordium Dubnium Seaborgium Bohrium Hassium Meitnerium Darmstadtium Roentgenium Copernicium Nihonium Flerovium Moscovium Livermorium Tennessine Oganesson
Ununennium Unbinilium
Unquadtrium Unquadquadium Unquadpentium Unquadhexium Unquadseptium Unquadoctium Unquadennium Unpentnilium Unpentunium Unpentbium Unpenttrium Unpentquadium Unpentpentium Unpenthexium Unpentseptium Unpentoctium Unpentennium Unhexnilium Unhexunium Unhexbium Unhextrium Unhexquadium Unhexpentium Unhexhexium Unhexseptium Unhexoctium Unhexennium Unseptnilium Unseptunium Unseptbium
Unbiunium Unbibium Unbitrium Unbiquadium Unbipentium Unbihexium Unbiseptium Unbioctium Unbiennium Untrinilium Untriunium Untribium Untritrium Untriquadium Untripentium Untrihexium Untriseptium Untrioctium Untriennium Unquadnilium Unquadunium Unquadbium
Element 119 (highlighted)
marks the start of theorizations

An extended periodic table theorizes about elements beyond element 118 (beyond period 7, or row 7). Currently seven periods in the periodic table of chemical elements are known and proven, culminating with atomic number 118. If further elements with higher atomic numbers than this are discovered, they will be placed in additional periods, laid out (as with the existing periods) to illustrate periodically recurring trends in the properties of the elements concerned. Any additional periods are expected to contain a larger number of elements than the seventh period, as they are calculated to have an additional so-called g-block, containing at least 18 elements with partially filled g-orbitals in each period. An eight-period table containing this block was suggested by Glenn T. Seaborg in 1969.[1][2] IUPAC defines an element to exist if its lifetime is longer than 10−14 seconds, which is the time it takes for the nucleus to form an electronic cloud.[3]

No elements in this region have been synthesized or discovered in nature.[4] The first element of the g-block may have atomic number 121, and thus would have the systematic name unbiunium. Elements in this region are likely to be highly unstable with respect to radioactive decay, and have extremely short half lives, although element 126 is hypothesized to be within an island of stability that is resistant to fission but not to alpha decay. It is not clear how many elements beyond the expected island of stability are physically possible, if period 8 is complete, or if there is a period 9.

According to the orbital approximation in quantum mechanical descriptions of atomic structure, the g-block would correspond to elements with partially filled g-orbitals. However, spin-orbit coupling effects reduce the validity of the orbital approximation substantially for elements of high atomic number. While Seaborg's version of the extended period had the heavier elements following the pattern set by lighter elements, as it did not take into account relativistic effects, models that take relativistic effects into account do not. Pekka Pyykkö and B. Fricke used computer modeling to calculate the positions of elements up to Z = 184 (comprising periods 8, 9, and the beginning of 10), and found that several were displaced from the Madelung rule.[5][6]

History

It is unknown how far the periodic table might extend beyond the known 118 elements. Glenn T. Seaborg suggested that the highest possible element may be under Z = 130.[7] However, Walter Greiner predicted that there may not be a highest possible element.[8]

All of these hypothetical undiscovered elements are named by the International Union of Pure and Applied Chemistry (IUPAC) systematic element name standard which creates a generic name for use until the element has been discovered, confirmed, and an official name approved. However, typically they are not even named at all in the scientific literature, and are simply referred to by their atomic numbers; hence, element 164 would usually not be called "unhexquadium" (the IUPAC systematic name), but rather "element 164" with symbol "164", "(164)", or "E164".

As of April 2011, synthesis has been attempted for only ununennium, unbinilium, unbibium, unbiquadium, unbihexium, and unbiseptium. (Z = 119, 120, 122, 124, 126, and 127)

At element 118, the orbitals 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, 5s, 5p, 5d, 5f, 6s, 6p, 6d, 7s and 7p are assumed to be filled, with the remaining orbitals unfilled. The orbitals of the eighth period are predicted to be filled in the order 8s, 5g, 6f, 7d, 8p. However, after approximately element 120, the proximity of the electron shells makes placement in a simple table problematic.

Not all models show the higher elements following the pattern established by lighter elements. Pekka Pyykkö, for example, used computer modeling to calculate the positions of elements up to Z=172, and found that several were displaced from the Madelung energy-ordering rule.[6] He predicts that the orbital shells will fill up in this order:

  • 8s,
  • 5g,
  • the first two spaces of 8p,
  • 6f,
  • 7d,
  • 9s,
  • the first two spaces of 9p,
  • the rest of 8p.

He also suggests that period 8 be split into three parts:

  • 8a, containing 8s,
  • 8b, containing the first two elements of 8p,
  • 8c, containing 7d and the rest of 8p.[9]

Fricke et al. also predicted the extended periodic table up to 184.[5] This model has been more widely used among scientists and is shown above as the main form of the extended periodic table. Template:Extended periodic table (by Pyykkö, 50 columns, periods 8–9)

Predicted properties of undiscovered elements

Element 118 is the last element that has been claimed to have been synthesized. The next two elements, elements 119 and 120, should form an 8s series and be an alkali and alkaline earth metal respectively. Beyond element 120, the superactinide series is expected to begin, when the 8s electrons and the filling 8p1/2, 7d3/2, 6f5/2, and 5g7/2 subshells determine the chemistry of these elements. Complete and accurate CCSD calculations are not available for elements beyond 122 because of the extreme complexity of the situation: the 5g, 6f, and 7d orbitals should have about the same energy level, and in the region of element 160 the 9s, 8p3/2, and 9p1/2 orbitals should also be about equal in energy. This will cause the electron shells to mix so that the block concept no longer applies very well, and will also result in novel chemical properties that will make positioning these elements in a periodic table very difficult. For example, element 164 is expected to mix characteristics of the elements of group 10, 12, 14, and 18.[10]

Chemical and physical properties

8s elements

Some predicted properties of elements 119 and 120[5][10]
Property 119 120
Relative atomic mass [322] [325]
Group 1 2
Valence electron configuration 8s1 8s2
Stable oxidation states 1, 3 2, 4
First ionization energy 437.1 kJ/mol 578.9 kJ/mol
Metallic radius 260 pm 200 pm
Density 3 g/cm3 7 g/cm3
Melting point 0–30 °C 680 °C
Boiling point 630 °C 1700 °C

The first two elements of period 8 are expected to be ununennium and unbinilium, elements 119 and 120. Their electron configurations should have the 8s shell being filled. However, the 8s orbital is relativistically stabilized and contracted and thus, elements 119 and 120 should be more like caesium and barium than their immediate neighbours above, francium and radium. Another effect of the relativistic contraction of the 8s orbital is that the atomic radii of these two elements should be about the same of those of francium and radium. They should behave like normal alkali and alkaline earth metals, normally forming +1 and +2 oxidation states respectively, but the relativistic destabilization of the 7p3/2 subshell and the relatively low ionization energies of the 7p3/2 electrons should make higher oxidation states like +3 and +4 (respectively) possible as well.[5][10]

Superactinides

The superactinide series is expected to contain elements 121 to 155. In the superactinide series, the 7d3/2, 8p1/2, 6f5/2 and 5g7/2 shells should all fill simultaneously:[11] this creates very complicated situations, so much so that complete and accurate CCSD calculations have been done only for elements 121 and 122.[10] The first superactinide, unbiunium (element 121), should be a congener of lanthanum and actinium and should have similar properties to them:[12] its main oxidation state should be +3, although the closeness of the valence subshells' energy levels may permit higher oxidation states, just like in elements 119 and 120.[10] However, relativistically stabilization of the 8p subshell should result in a ground-state 8s28p1 valence electron configuration for element 121, in contrast to the ds2 configurations of lanthanum and actinium.[10] Its first ionization energy is predicted to be 429.4 kJ/mol, which would be lower than those of all known elements except for the alkali metals potassium, rubidium, caesium, and francium: this value is even lower than that of the period 8 alkali metal ununennium (463.1 kJ/mol). Similarly, the next superactinide, unbibium (element 122), may be a congener of cerium and thorium, with a main oxidation state of +4, but would have a ground-state 7d18s28p1 valence electron configuration, unlike thorium's 6d27s2 configuration. Hence, its first ionization energy would be smaller than thorium's (Th: 6.54 eV; Ubb: 5.6 eV) because of the greater ease of ionizing unbibium's 8p1/2 electron than thorium's 7s electron.[10]

In the first few superactinides, the binding energies of the added electrons are predicted to be small enough that they can lose all their valence electrons; for example, unbihexium (element 126) could easily form a +8 oxidation state, and even higher oxidation states for the next few elements may be possible. Unbihexium is also predicted to display a variety of other oxidation states: recent calculations have suggested a stable monofluoride UbhF may be possible, resulting from a bonding interaction between the 5g orbital on unbihexium and the 2p orbital on fluorine.[13] Other predicted oxidation states include +2, +4, and +6; +4 is expected to be the most usual oxidation state of unbihexium.[11] The presence of electrons in g-orbitals, which do not exist in the ground state electron configuration of any currently known element, should allow presently unknown hybrid orbitals to form and influence the chemistry of the superactinides in new ways, although the absence of g electrons in known elements makes predicting their chemistry more difficult.[5]

Some predicted compounds of the superactinides (X = a halogen)[9]
121 122 123 124 125 126 132 142 143 144 145 146 148 153 154 155
Compound UbuX3 UbbX4 UbtX5 UbqX6 UbpX6 UbhF
UbhF6
UbhO4
UqbX4
UqbX6
UqtF6 UqqX6
UqqO2+
2

UqqF8
UqqO4
UqpF6 UqoO6
Analogs LaX3
AcX3
CeX4
ThX4
ThF4 UF6
UO2+
2

PuF8
PuO4
UO6
Oxidation states 3 4 5 6 6 1, 2, 4, 6, 8 6 4, 6 6, 8 3, 4, 5, 6, 8 6 8 12 3 0, 2 3, 5

In the later superactinides, the oxidation states should become lower. By element 132, the predominant most stable oxidation state will be only +6; this is further reduced to +3 and +4 by element 144, and at the end of the superactinide series it will be only +2 (and possibly even 0) because the 6f shell, which is being filled at that point, is deep inside the electron cloud and the 8s and 8p1/2 electrons are bound too strongly to be chemically active. The 5g shell should be filled at element 144 and the 6f shell at around element 154, and at this region of the superactinides the 8p1/2 electrons are bound so strongly that they are no longer active chemically, so that only a few electrons can participate in chemical reactions. Calculations by Fricke et al. predict that at element 154, the 6f shell is full and there are no d- or other electron wave functions outside the chemically inactive 8s and 8p1/2 shells. This would cause element 154 to be very unreactive, so that it may exhibit properties similar to those of the noble gases.[5][10]

Similarly to the lanthanide and actinide contractions, there should be a superactinide contraction in the superactinide series where the ionic radii of the superactinides are smaller than expected. In the lanthanides, the contraction is about 4.4 pm per element; in the actinides, it is about 3 pm per element. The contraction is larger in the lanthanides than in the actinides due to the greater localization of the 4f wave function as compared to the 5f wave function. Comparisons with the wave functions of the outer electrons of the lanthanides, actinides, and superactinides lead to a prediction of a contraction of about 2 pm per element in the superactinides; although this is smaller than the contractions in the lanthanides and actinides, its total effect is larger due to the fact that 32 electrons are filled in the deeply buried 5g and 6f shells, instead of just 14 electrons being filled in the 4f and 5f shells in the lanthanides and actinides respectively.[5]

Pekka Pyykkö divides these superactinides into three series: a 5g series (elements 121 to 138), an 8p1/2 series (elements 139 to 140), and a 6f series (elements 141 to 155), although noting that there would be a great deal of overlapping between energy levels and that the 6f, 7d, or 8p1/2 orbitals could well also be occupied in the early superactinide atoms or ions. He also expects that they would behave more like "superlanthanides", in the sense that the 5g electrons would mostly be chemically inactive, similarly to how only one or two 4f electrons in each lanthanide are ever ionized in chemical compounds. He also predicted that the possible oxidation states of the superactinides might rise very high in the 6f series, to values such as +12 in element 148.[9]

7d transition metals

The transition metals in period 8 are expected to be elements 156 to 164. Although the 8s and 8p1/2 electrons are bound so strongly in these elements that they should not be able to take part in any chemical reactions, the 9s and 9p1/2 levels are expected to be readily available for hybridization such that these elements will still behave chemically like their lighter homologues in the periodic table, showing the same oxidation states as they do, in contrast to earlier predictions which predicted the period 8 transition metals to have main oxidation states two less than those of their lighter congeners.[5][10]

The noble metals of this series of transition metals are not expected to be as noble as their lighter homologues, due to the absence of an outer s shell for shielding and also because the 7d shell is strongly split into two subshells due to relativistic effects. This causes the first ionization energies of the 7d transition metals to be smaller than those of their lighter congeners.[5][10][11]

Calculations predict that the 7d electrons of element 164 (unhexquadium) should participate very readily in chemical reactions, so that unhexquadium should be able to show stable +6 and +4 oxidation states in addition to the normal +2 state in aqueous solutions with strong ligands. Unhexquadium should thus be able to form compounds like Uhq(CO)4, Uhq(PF3)4 (both tetrahedral), and Uhq(CN)2−
2
(linear), which is very different behavior from that of lead, which unhexquadium would be a heavier homologue of if not for relativistic effects. Nevertheless, the divalent state would be the main one in aqueous solution, and unhexquadium(II) should behave more similarly to lead than unhexquadium(IV) and unhexquadium(VI).[10][11]

Unhexquadium should be a soft metal like mercury, and metallic unhexquadium should have a high melting point as it is predicted to bond covalently. It is also expected to be a soft Lewis acid and have Ahrlands softness parameter close to 4 eV. It should also have some similarities to ununoctium as well as to the other group 12 elements.[10] Unhexquadium should be at most moderately reactive, having a first ionization energy that should be around 685 kJ/mol, comparable to that of molybdenum.[5][11] Due to the lanthanide, actinide, and superactinide contractions, unhexquadium should have an metallic radius of only 158 pm, very close to that of the much lighter magnesium, despite its being expected to have an atomic weight of around 474 u, about 19.5 times as much as that of magnesium.[5] This small radius and high weight cause it to be expected to have an extremely high density of around 46 g·cm−3, over twice that of osmium, currently the most dense element known, at 22.61 g·cm−3; unhexquadium should be the second most dense element in the first 172 elements in the periodic table, with only its neighbour unhextrium (element 163) being more dense (at 47 g·cm−3).[5] Metallic unhexquadium should be quite stable, as the 8s and 8p1/2 electrons are very deeply buried in the electron core and only the 7d electrons are available for bonding. Metallic unhexquadium should have a very large cohesive energy (enthalpy of crystallization) due to its covalent bonds, most probably resulting in a high melting point.[11]

Theoretical interest in the chemistry of unhexquadium is largely motivated by theoretical predictions that it, especially the isotope 482Uhq (with 164 protons and 318 neutrons), would be at the center of a hypothetical second island of stability (the first being centered on 306Ubb).[14][15][16]

Some predicted properties of the 7d transition metals. The metallic radii and densities are first approximations. X represents a halogen.[5][9][10]
Most analogous group is given first, followed by other similar groups.[11]
Property 156 157 158 159 160 161 162 163 164
Relative atomic mass [445] [448] [452] [456] [459] [463] [466] [470] [474]
Group 4
(Yb group?)
5
(3)
6
(4)
7
(5)
8
(6)
9
(7)
10
(8)
11
(9)
12
(10, 14, 18)
Valence electron configuration 7d2 7d3 7d4 7d4 9s1 7d5 9s1 7d6 9s1 7d8 7d9 7d10
Stable oxidation states 2, 4 3, 5 4, 6, 8 1, 5, 7 2, 6, 8 3, 7 4, 8 3, 5 0, 2, 4, 6
First ionization energy 395.6 kJ/mol 453.5 kJ/mol 521.0 kJ/mol 337.7 kJ/mol 424.5 kJ/mol 472.8 kJ/mol 559.6 kJ/mol 617.5 kJ/mol 685.0 kJ/mol
Metallic radius 170 pm 163 pm 157 pm 152 pm 148 pm 148 pm 149 pm 152 pm 158 pm
Density 26 g/cm3 28 g/cm3 30 g/cm3 33 g/cm3 36 g/cm3 40 g/cm3 45 g/cm3 47 g/cm3 46 g/cm3
Predicted compounds UpoX6
UpoX8
UpoO4
UhnO4 UhqX2
UhqX4
...
Analogs WF6, SgF6 OsO4, HsO4 HgX2
HgF4

Elements 165 to 172

Elements 165 (unhexpentium) and 166 (unhexhexium) should behave as normal alkali and alkaline earth metals when in the +1 and +2 oxidation states respectively. The 9s electrons should have ionization energies comparable to those of the 3s electrons of sodium and magnesium, due to relativistic effects causing the 9s electrons to be much more strongly bound than non-relativistic calculations would predict. Elements 165 and 166 should normally exhibit the +1 and +2 oxidation states respectively; however, the ionization energies of the 7d electrons are low enough to allow higher oxidation states like +3 and +4 to also occur quite commonly.[5][10]

In elements 167 to 172, the 9p1/2 and 8p3/2 shells will be filled. Their energy eigenvalues are so close together that they behaves as one combined p shell, similar to the non-relativistic 2p and 3p shells. Thus, the inert pair effect does not occur and the most common oxidation states of elements 167 to 170 should be +3, +4, +5, and +6 respectively. Element 171 (unseptunium) is expected to be a halogen, showing various oxidation states ranging from –1 to +7. Its electron affinity should be 3.0 eV, allowing it to form a hydrogen halide, HUsu. The Usu ion is expected to be a soft base, comparable to iodide (I). Element 172 (unseptbium) should be a noble gas with chemical behaviour similar to that of xenon, as their ionization energies should be very similar (Xe, 1170.4 kJ/mol; Usb, 1090.3 kJ/mol). The only main difference between them is that element 172, unlike xenon, is expected to be a liquid or a solid at standard temperature and pressure due to its much higher atomic weight.[5] Unseptbium should be a strong Lewis acid, forming fluorides and oxides, similarly to its lighter congener xenon.[11] Because of this analogy of elements 165–172 to periods 2 and 3, Fricke et al. considered them to form a ninth period of the periodic table, while the eighth period was taken by them to end at the noble metal element 164. This ninth period would be similar to the second and third period in that it should have no transition metals.[11]

Some predicted properties of elements 165–172. The metallic or covalent radii and densities are first approximations.[5][10]
Most analogous group is given first, followed by other similar groups.[11]
Property 165 166 167 168 169 170 171 172
Relative atomic mass [477] [481] [485] [489] [493] [496] [500] [504]
Group 1
(11, 13)
2
(12, 14)
13 14 15 16 17 18
Valence electron configuration 9s1 9s2 9s2 9p1 9s2 9p2 9s2 9p2 8p1 9s2 9p2 8p2 9s2 9p2 8p3 9s2 9p2 8p4
Stable oxidation states 1, 3 2, 4 3 4 5 6 −1, 3, 7 0, 4, 6, 8
First ionization energy 521.0 kJ/mol 627.2 kJ/mol 617.5 kJ/mol 723.6 kJ/mol 800.8 kJ/mol 887.7 kJ/mol 984.2 kJ/mol 1090.3 kJ/mol
Metallic or covalent radius 250 pm 200 pm 190 pm 180 pm 175 pm 170 pm 165 pm 220 pm
Density 7 g/cm3 11 g/cm3 17 g/cm3 19 g/cm3 18 g/cm3 17 g/cm3 16 g/cm3 9 g/cm3

"Eka-superactinides"

Immediately after element 172 (unseptbium), the first noble gas after element 118 (the last period 7 element), another long transition series like the superactinides should begin, filling the 6g, 7f, 8d, and perhaps 6h shells. These electrons would be very loosely bound, rendering extremely high oxidation states possibly easy to reach.[11] This series may be termed the eka-superactinides, as it is the next long transition series in the periodic table after the superactinides.

The ground-state electron configuration of element 184 (unoctquadium) is expected to be [Usb]6g57f48d3: only the 8d and 7f electrons should be chemically active, with possible reasons being small radial extension and large binding energy. The absence of 6h11/2, 10s, and 10p1/2 electrons from this ground-state electron configuration suggests that it would behave chemically simpler than the early superactinides, and more similar to uranium or neptunium. As more electrons are ionized, the number of 6g electrons in the unoctquadium ion will increase: these are buried in the electron core and would not participate in chemical reactions, but the 7f electrons could. Extrapolation from uranium suggests that the +4 state would be the most stable in aqueous solution, with +5 and +6 readily obtainable in solid compounds. Higher states would necessitate the ionization of the deeply buried 6g electrons and are probably unlikely: furthermore, their binding energy becomes much higher as more electrons are removed. This effect is so important that the 9s and 9p1/2 electrons, part of the closed [Usb] electron core, would enter the 6g subshell in the +8 oxidation state and higher. This suggests that the multitude of simultaneously-filling outer electron shells as one proceeds down a long transition series might not lead to exceptionally high or exotic oxidation states, nor should it lead to anomalously low increases in ionization energy.[5][11] This contradicts preliminary extrapolations (without calculation) that expected that unoctquadium would have many oxidation states ranging from +4 (with 8 6g electrons) to +12 (with no 6g electrons).[17]

Nuclear properties

The first island of stability is expected to be centered on unbibium-306 (with 122 protons and 184 neutrons),[14] and the second is expected to be centered on unhexquadium-482 (with 164 protons and 318 neutrons).[15][16] This second island of stability should confer additional stability on elements 152–168.[11]

Calculations according to the Hartree–Fock–Bogoliubov Method using the non-relativistic Skyrme interaction have proposed Z=126 as a closed proton shell. In this region of the periodic table, N=184 and N=196 have been suggested as closed neutron shells. Therefore the isotopes of most interest are 310Ubh and 322Ubh, for these might be considerably longer-lived than other isotopes. Unbihexium, having a magic number of protons, is predicted to be more stable than other elements in this region, and may have nuclear isomers with very long half-lives.[18]

Electron configurations

The following are the expected electron configurations of elements 119–172 and 184.[11]

Chemical element Chemical series Electron configuration
(predicted)
[10][11]
119 Uue Ununennium Alkali metal [Uuo] 8s1
120 Ubn Unbinilium Alkaline earth metal [Uuo] 8s2
121 Ubu Unbiunium Superactinide [Uuo] 8s2 8p1
1/2
122 Ubb Unbibium Superactinide [Uuo] 7d1 8s2 8p1
1/2
123 Ubt Unbitrium Superactinide [Uuo] 6f1 7d1 8s2 8p1
1/2
124 Ubq Unbiquadium Superactinide [Uuo] 6f3 8s2 8p1
1/2
125 Ubp Unbipentium Superactinide [Uuo] 5g1 6f3 8s2 8p1
1/2
126 Ubh Unbihexium Superactinide [Uuo] 5g2 6f2 7d1 8s2 8p1
1/2
127 Ubs Unbiseptium Superactinide [Uuo] 5g3 6f2 8s2 8p2
1/2
128 Ubo Unbioctium Superactinide [Uuo] 5g4 6f2 8s2 8p2
1/2
129 Ube Unbiennium Superactinide [Uuo] 5g5 6f2 8s2 8p2
1/2
130 Utn Untrinilium Superactinide [Uuo] 5g6 6f2 8s2 8p2
1/2
131 Utu Untriunium Superactinide [Uuo] 5g7 6f2 8s2 8p2
1/2
132 Utb Untribium Superactinide [Uuo] 5g8 6f2 8s2 8p2
1/2
133 Utt Untritrium Superactinide [Uuo] 5g8 6f3 8s2 8p2
1/2
134 Utq Untriquadium Superactinide [Uuo] 5g8 6f4 8s2 8p2
1/2
135 Utp Untripentium Superactinide [Uuo] 5g9 6f4 8s2 8p2
1/2
136 Uth Untrihexium Superactinide [Uuo] 5g10 6f4 8s2 8p2
1/2
137 Uts Untriseptium Superactinide [Uuo] 5g11 6f3 7d1 8s2 8p2
1/2
138 Uto Untrioctium Superactinide [Uuo] 5g12 6f3 7d1 8s2 8p2
1/2
139 Ute Untriennium Superactinide [Uuo] 5g13 6f2 7d2 8s2 8p2
1/2
140 Uqn Unquadnilium Superactinide [Uuo] 5g14 6f3 7d1 8s2 8p2
1/2
141 Uqu Unquadunium Superactinide [Uuo] 5g15 6f2 7d2 8s2 8p2
1/2
142 Uqb Unquadbium Superactinide [Uuo] 5g16 6f2 7d2 8s2 8p2
1/2
143 Uqt Unquadtrium Superactinide [Uuo] 5g17 6f2 7d2 8s2 8p2
1/2
144 Uqq Unquadquadium Superactinide [Uuo] 5g18 6f1 7d3 8s2 8p2
1/2
145 Uqp Unquadpentium Superactinide [Uuo] 5g18 6f3 7d2 8s2 8p2
1/2
146 Uqh Unquadhexium Superactinide [Uuo] 5g18 6f4 7d2 8s2 8p2
1/2
147 Uqs Unquadseptium Superactinide [Uuo] 5g18 6f5 7d2 8s2 8p2
1/2
148 Uqo Unquadoctium Superactinide [Uuo] 5g18 6f6 7d2 8s2 8p2
1/2
149 Uqe Unquadennium Superactinide [Uuo] 5g18 6f6 7d3 8s2 8p2
1/2
150 Upn Unpentnilium Superactinide [Uuo] 5g18 6f6 7d4 8s2 8p2
1/2
151 Upu Unpentunium Superactinide [Uuo] 5g18 6f8 7d3 8s2 8p2
1/2
152 Upb Unpentbium Superactinide [Uuo] 5g18 6f9 7d3 8s2 8p2
1/2
153 Upt Unpenttrium Superactinide [Uuo] 5g18 6f11 7d2 8s2 8p2
1/2
154 Upq Unpentquadium Superactinide [Uuo] 5g18 6f12 7d2 8s2 8p2
1/2
155 Upp Unpentpentium Superactinide [Uuo] 5g18 6f13 7d2 8s2 8p2
1/2
156 Uph Unpenthexium Transition metal [Uuo] 5g18 6f14 7d2 8s2 8p2
1/2
157 Ups Unpentseptium Transition metal [Uuo] 5g18 6f14 7d3 8s2 8p2
1/2
158 Upo Unpentoctium Transition metal [Uuo] 5g18 6f14 7d4 8s2 8p2
1/2
159 Upe Unpentennium Transition metal [Uuo] 5g18 6f14 7d4 8s2 8p2
1/2
9s1
160 Uhn Unhexnilium Transition metal [Uuo] 5g18 6f14 7d5 8s2 8p2
1/2
9s1
161 Uhu Unhexunium Transition metal [Uuo] 5g18 6f14 7d6 8s2 8p2
1/2
9s1
162 Uhb Unhexbium Transition metal [Uuo] 5g18 6f14 7d8 8s2 8p2
1/2
163 Uht Unhextrium Transition metal [Uuo] 5g18 6f14 7d9 8s2 8p2
1/2
164 Uhq Unhexquadium Transition metal [Uuo] 5g18 6f14 7d10 8s2 8p2
1/2
165 Uhp Unhexpentium Alkali metal [Uuo] 5g18 6f14 7d10 8s2 8p2
1/2
9s1
166 Uhh Unhexhexium Alkaline earth metal [Uuo] 5g18 6f14 7d10 8s2 8p2
1/2
9s2
167 Uhs Unhexseptium Post-transition metal [Uuo] 5g18 6f14 7d10 8s2 8p2
1/2
9s2 9p1
1/2
168 Uho Unhexoctium Post-transition metal [Uuo] 5g18 6f14 7d10 8s2 8p2
1/2
9s2 9p2
1/2
169 Uhe Unhexennium Post-transition metal [Uuo] 5g18 6f14 7d10 8s2 8p2
1/2
8p1
3/2
9s2 9p2
1/2
170 Usn Unseptnilium Post-transition metal [Uuo] 5g18 6f14 7d10 8s2 8p2
1/2
8p2
3/2
9s2 9p2
1/2
171 Usu Unseptunium Diatomic nonmetal [Uuo] 5g18 6f14 7d10 8s2 8p2
1/2
8p3
3/2
9s2 9p2
1/2
172 Usb Unseptbium Noble gas [Uuo] 5g18 6f14 7d10 8s2 8p2
1/2
8p4
3/2
9s2 9p2
1/2
173–183 ... ... Eka-superactinide ...
184 Uoq Unoctquadium Eka-superactinide [Usb] 6g5 7f4 8d3

Attempts to synthesize still undiscovered elements

The only period 8 elements that have had synthesis attempts were elements 119, 120, 122, 124, 126, and 127. So far, none of these synthesis attempts were successful.

Ununennium

The synthesis of ununennium was attempted in 1985 by bombarding a target of einsteinium-254 with calcium-48 ions at the superHILAC accelerator at Berkeley, California:

No atoms were identified, leading to a limiting yield of 300 nb.[19] As of May 2012, plans are under way to attempt to synthesize the isotopes 295Uue and 296Uue by bombarding a target of berkelium with titanium at the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt, Germany:[20][21]

Unbinilium

Attempts to date to synthesize the element using fusion reactions at low excitation energy have met with failure, although there are reports that the fission of nuclei of unbinilium at very high excitation has been successfully measured, indicating a strong shell effect at Z=120. In March–April 2007, the synthesis of unbinilium was attempted at the Flerov Laboratory of Nuclear Reactions in Dubna by bombarding a plutonium-244 target with iron-58 ions.[22] Initial analysis revealed that no atoms of element 120 were produced providing a limit of 400 fb for the cross section at the energy studied.[23]

The Russian team are planning to upgrade their facilities before attempting the reaction again.[21]

In April 2007, the team at GSI attempted to create unbinilium using uranium-238 and nickel-64:[21]

No atoms were detected providing a limit of 1.6 pb on the cross section at the energy provided. The GSI repeated the experiment with higher sensitivity in three separate runs from April–May 2007, Jan–March 2008, and Sept–Oct 2008, all with negative results and providing a cross section limit of 90 fb.[21]

In June–July 2010, scientists at the GSI attempted the fusion reaction:[21]

They were unable to detect any atoms but exact details are not currently available.[21]

In August–October 2011, a different team at the GSI using the TASCA facility tried the new reaction:[21]

Results from this experiment are not yet available.[21] In 2008, the team at GANIL, France, described the results from a new technique which attempts to measure the fission half-life of a compound nucleus at high excitation energy, since the yields are significantly higher than from neutron evaporation channels. It is also a useful method for probing the effects of shell closures on the survivability of compound nuclei in the super-heavy region, which can indicate the exact position of the next proton shell (Z=114, 120, 124, or 126). The team studied the nuclear fusion reaction between uranium ions and a target of natural nickel:

The results indicated that nuclei of unbinilium were produced at high (~70 MeV) excitation energy which underwent fission with measurable half-lives > 10−18 s. Although very short, the ability to measure such a process indicates a strong shell effect at Z=120. At lower excitation energy (see neutron evaporation), the effect of the shell will be enhanced and ground-state nuclei can be expected to have relatively long half-lives. This result could partially explain the relatively long half-life of 294Uuo measured in experiments at Dubna. Similar experiments have indicated a similar phenomenon at Z=124 (see unbiquadium) but not for flerovium, suggesting that the next proton shell does in fact lie at Z>120.[24][25] The team at RIKEN have begun a program utilizing 248Cm targets and have indicated future experiments to probe the possibility of Z=120 being the next magic number using the aforementioned nuclear reactions to form 302Ubn.[26]

Unbibium

The first attempt to synthesize unbibium was performed in 1972 by Flerov et al. at JINR, using the hot fusion reaction:[27]

No atoms were detected and a yield limit of 5 mb (5,000,000,000 pb) was measured. Current results (see flerovium) have shown that the sensitivity of this experiment was too low by at least 6 orders of magnitude.[citation needed]

In 2000, the Gesellschaft für Schwerionenforschung (GSI) performed a very similar experiment with much higher sensitivity:[27]

These results indicate that the synthesis of such heavier elements remains a significant challenge and further improvements of beam intensity and experimental efficiency is required. The sensitivity should be increased to 1 fb.[citation needed]

Another unsuccessful attempt to synthesize unbibium was carried out in 1978 at the GSI, where a natural erbium target was bombarded with xenon-136 ions:[27]

The two attempts in the 1970s to synthesize unbibium were caused by research investigating whether superheavy elements could potentially be naturally occurring.[27] Several experiments have been performed between 2000-2004 at the Flerov laboratory of Nuclear Reactions studying the fission characteristics of the compound nucleus 306Ubb. Two nuclear reactions have been used, namely 248Cm + 58Fe and 242Pu + 64Ni.[27] The results have revealed how nuclei such as this fission predominantly by expelling closed shell nuclei such as 132Sn (Z=50, N=82). It was also found that the yield for the fusion-fission pathway was similar between 48Ca and 58Fe projectiles, indicating a possible future use of 58Fe projectiles in superheavy element formation.[28]

Unbiquadium

In a series of experiments, scientists at GANIL have attempted to measure the direct and delayed fission of compound nuclei of elements with Z=114, 120, and 124 in order to probe shell effects in this region and to pinpoint the next spherical proton shell. This is because having complete nuclear shells (or, equivalently, having a magic number of protons or neutrons) would confer more stability on the nuclei of such superheavy elements, thus moving closer to the island of stability. In 2006, with full results published in 2008, the team provided results from a reaction involving the bombardment of a natural germanium target with uranium ions:

The team reported that they had been able to identify compound nuclei fissioning with half-lives > 10−18 s. This result suggests a strong stabilizing effect at Z=124 and points to the next proton shell at Z>120, not at Z=114 as previously thought. A compound nucleus is a loose combination of nucleons that have not arranged themselves into nuclear shells yet. It has no internal structure and is held together only by the collision forces between the target and projectile nuclei. It is estimated that it requires around 10−14 s for the nucleons to arrange themselves into nuclear shells, at which point the compound nucleus becomes an nuclide, and this number is used by IUPAC as the minimum half-life a claimed isotope must have to potentially be recognised as being discovered. Thus, the GANIL experiments do not count as a discovery of element 124.[27]

Unbihexium

The first and only attempt to synthesize unbihexium, which was unsuccessful, was performed in 1971 at CERN by René Bimbot and John M. Alexander using the hot fusion reaction:[27]

232
90
Th
+ 84
36
Kr
316
126
Ubh
* → no atoms

A high energy alpha particle was observed and taken as possible evidence for the synthesis of unbihexium. Recent research[which?] suggests that this is highly unlikely as the sensitivity of experiments performed in 1971 would have been several orders of magnitude too low according to current understanding.

Unbiseptium

Unbiseptium has had one failed attempt at synthesis in 1978 at the Darmstadt UNILAC accelerator by bombarding a natural tantalum target with xenon ions:[27]

Possible natural occurrence

On April 24, 2008, a group led by Amnon Marinov at the Hebrew University of Jerusalem claimed to have found single atoms of unbibium-292 in naturally occurring thorium deposits at an abundance of between 10−11 and 10−12, relative to thorium.[29] The claim of Marinov et al. was criticized by a part of the scientific community, and Marinov says he has submitted the article to the journals Nature and Nature Physics but both turned it down without sending it for peer review.[30] The unbibium-292 atoms were claimed to be superdeformed or hyperdeformed isomers, with a half-life of at least 100 million years.[27]

A criticism of the technique, previously used in purportedly identifying lighter thorium isotopes by mass spectrometry,[31] was published in Physical Review C in 2008.[32] A rebuttal by the Marinov group was published in Physical Review C after the published comment.[33]

A repeat of the thorium-experiment using the superior method of Accelerator Mass Spectrometry (AMS) failed to confirm the results, despite a 100-fold better sensitivity.[34] This result throws considerable doubt on the results of the Marinov collaboration with regards to their claims of long-lived isotopes of thorium,[31] roentgenium[35] and unbibium.[29] It is still possible that traces of unbibium might only exist in some thorium samples, although this is unlikely.[27]

It was suggested in 1976 that primordial superheavy elements (mainly livermorium, unbiquadium, unbihexium, and unbiseptium) could be a cause of unexplained radiation damage in minerals. This prompted many researchers to search for it in nature from 1976 to 1983. Some claimed that they had detected alpha particles with the right energies to cause the damage observed, supporting the presence of unbihexium, while some claimed that no unbihexium had been detected. However, the possible extent of primordial unbihexium on Earth is uncertain; it might now only exist in traces, or could even have completely decayed by now after having caused the radiation damage long ago.[18]

End of the periodic table

The number of physically possible elements is unknown. A low estimate is that the periodic table may end soon after the island of stability,[7] which is expected to center on Z = 126, as the extension of the periodic and nuclides tables is restricted by the proton and the neutron drip lines;[36] however, some, such as Walter Greiner, predict that there may not be an end to the periodic table at all.[8] Other predictions of an end to the periodic table include Z = 128 (John Emsley) and Z = 155 (Albert Khazan).[27]

Feynmanium and elements above the atomic number 137

Richard Feynman noted[37] that a simplistic interpretation of the relativistic Dirac equation runs into problems with electron orbitals at Z > 1/α ≈ 137 as described in the sections below, 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. On the other hand, a more rigorous analysis calculates the limit to be Z ≈ 173, and also that this limit would not actually spell the end of the periodic table.

Bohr model

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

where Z is the atomic number, and α is the fine structure constant, a measure of the strength of electromagnetic interactions.[38] 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.

Relativistic Dirac equation

The relativistic Dirac equation gives the ground state energy as

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.[39] 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 (1s) 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.[40] However, this does not happen if the innermost orbital is filled, so that Z = 173 does not constitute a limit to the periodic table, only a limit to fully ionized nuclei.[8]

See also

References

  1. ^ Seaborg, Glenn T. (August 26, 1996). "An Early History of LBNL".
  2. ^ Frazier, K. (1978). "Superheavy Elements". Science News. 113 (15): 236–238. doi:10.2307/3963006. JSTOR 3963006.
  3. ^ Kernchemie
  4. ^ Element 122 was claimed to exist naturally in April 2008, but this claim was widely believed to be erroneous. "Heaviest element claim criticised". Rsc.org. 2008-05-02. Retrieved 2010-03-16.
  5. ^ a b c d e f g h i j k l m n o p q Fricke, B.; Greiner, W.; Waber, J. T. (1971). "The continuation of the periodic table up to Z = 172. The chemistry of superheavy elements". Theoretica chimica acta. 21 (3). Springer-Verlag: 235–260. doi:10.1007/BF01172015. Retrieved 28 November 2012.
  6. ^ a b "Extended elements: new periodic table". 2010.
  7. ^ a b Seaborg, Glenn T. (c. 2006). "transuranium element (chemical element)". Encyclopædia Britannica. Retrieved 2010-03-16.
  8. ^ a b c Philip Ball (November 2010). "Would element 137 really spell the end of the periodic table? Philip Ball examines the evidence". Chemistry World. Royal Society of Chemistry. Retrieved 2012-09-30.
  9. ^ a b c d Pyykkö, Pekka (2011). "A suggested periodic table up to Z≤ 172, based on Dirac–Fock calculations on atoms and ions". Physical Chemistry Chemical Physics. 13 (1): 161–8. Bibcode:2011PCCP...13..161P. doi:10.1039/c0cp01575j. PMID 20967377.
  10. ^ a b c d e f g h i j k l m n o p Haire, Richard G. (2006). "Transactinides and the future elements". In Morss; Edelstein, Norman M.; Fuger, Jean (eds.). The Chemistry of the Actinide and Transactinide Elements (3rd ed.). Dordrecht, The Netherlands: Springer Science+Business Media. ISBN 1-4020-3555-1.{{cite book}}: CS1 maint: ref duplicates default (link)
  11. ^ a b c d e f g h i j k l m n o Fricke, Burkhard (1975). "Superheavy elements: a prediction of their chemical and physical properties". Recent Impact of Physics on Inorganic Chemistry. 21: 89–144. doi:10.1007/BFb0116498. Retrieved 4 October 2013.
  12. ^ Waber, J. T. (1969). "SCF Dirac–Slater Calculations of the Translawrencium Elements". The Journal of Chemical Physics. 51 (2): 664–661. Bibcode:1969JChPh..51..664W. doi:10.1063/1.1672054.
  13. ^ Jacoby, Mitch (2006). "As-yet-unsynthesized superheavy atom should form a stable diatomic molecule with fluorine". Chemical & Engineering News. 84 (10): 19. doi:10.1021/cen-v084n010.p019a. Retrieved 2008-01-14.
  14. ^ a b Kratz, J. V. (5 September 2011). The Impact of Superheavy Elements on the Chemical and Physical Sciences (PDF). 4th International Conference on the Chemistry and Physics of the Transactinide Elements. Retrieved 27 August 2013.
  15. ^ a b http://www.eurekalert.org/pub_releases/2008-04/acs-nse031108.php
  16. ^ a b http://link.springer.com/article/10.1007%2FBF01406719/lookinside/000.png
  17. ^ Penneman, R. A.; Mann, J. B.; Jørgensen, C. K. (February 1971). "Speculations on the chemistry of superheavy elements such as Z = 164". Chemical Physics Letters. 8 (4): 321–326. Bibcode:1971CPL.....8..321P. doi:10.1016/0009-2614(71)80054-4.
  18. ^ a b Emsley, John (2011). Nature's Building Blocks: An A-Z Guide to the Elements (New ed.). New York, NY: Oxford University Press. p. 592. ISBN 978-0-19-960563-7.
  19. ^ R. W. Lougheed, J. H. Landrum, E. K. Hulet, J. F. Wild, R. J. Dougan, A. D. Dougan, H. Gäggeler, M. Schädel, K. J. Moody, K. E. Gregorich, and G. T. Seaborg (1985). "Search for superheavy elements using 48Ca + 254Esg reaction". Physical Reviews C. 32 (5): 1760–1763. Bibcode:1985PhRvC..32.1760L. doi:10.1103/PhysRevC.32.1760.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  20. ^ Modern alchemy: Turning a line, The Economist
  21. ^ a b c d e f g h http://fias.uni-frankfurt.de/kollo/Duellmann_FIAS-Kolloquium.pdf
  22. ^ THEME03-5-1004-94/2009
  23. ^ Oganessian, Yu. Ts.; Utyonkov, V.; Lobanov, Yu.; Abdullin, F.; Polyakov, A.; Sagaidak, R.; Shirokovsky, I.; Tsyganov, Yu.; Voinov, A.; N.N. (2009). "Attempt to produce element 120 in the 244Pu+58Fe reaction". Phys. Rev. C. 79 (2): 024603. Bibcode:2009PhRvC..79b4603O. doi:10.1103/PhysRevC.79.024603. {{cite journal}}: Unknown parameter |displayauthors= ignored (|display-authors= suggested) (help)
  24. ^ Natowitz, Joseph (2008). "How stable are the heaviest nuclei?". Physics. 1: 12. Bibcode:2008PhyOJ...1...12N. doi:10.1103/Physics.1.12.
  25. ^ Morjean, M.; et al. (2008). "Fission Time Measurements: A New Probe into Superheavy Element Stability". Phys. Rev. Lett. 101 (7): 072701. Bibcode:2008PhRvL.101g2701M. doi:10.1103/PhysRevLett.101.072701. PMID 18764526.
  26. ^ see slide 11 in Future Plan of the Experimental Program on Synthesizing the Heaviest Element at RIKEN
  27. ^ a b c d e f g h i j k Emsley, John (2011). Nature's Building Blocks: An A-Z Guide to the Elements (New ed.). New York, NY: Oxford University Press. p. 588. ISBN 978-0-19-960563-7. Cite error: The named reference "emsley" was defined multiple times with different content (see the help page).
  28. ^ see Flerov lab annual reports 2000–2004 inclusive http://www1.jinr.ru/Reports/Reports_eng_arh.html
  29. ^ a b Marinov, A.; Rodushkin, I.; Kolb, D.; Pape, A.; Kashiv, Y.; Brandt, R.; Gentry, R. V.; Miller, H. W. (2008). "Evidence for a long-lived superheavy nucleus with atomic mass number A=292 and atomic number Z=~122 in natural Th". International Journal of Modern Physics E. 19: 131. arXiv:0804.3869. Bibcode:2010IJMPE..19..131M. doi:10.1142/S0218301310014662.
  30. ^ Royal Society of Chemistry, "Heaviest element claim criticised", Chemical World.
  31. ^ a b Marinov, A.; Rodushkin, I.; Kashiv, Y.; Halicz, L.; Segal, I.; Pape, A.; Gentry, R. V.; Miller, H. W.; Kolb, D.; Brandt, R. (2007). "Existence of long-lived isomeric states in naturally-occurring neutron-deficient Th isotopes". Phys. Rev. C. 76 (2): 021303(R). arXiv:nucl-ex/0605008. Bibcode:2007PhRvC..76b1303M. doi:10.1103/PhysRevC.76.021303.
  32. ^ R. C. Barber; J. R. De Laeter (2009). "Comment on "Existence of long-lived isomeric states in naturally-occurring neutron-deficient Th isotopes"". Phys. Rev. C. 79 (4): 049801. Bibcode:2009PhRvC..79d9801B. doi:10.1103/PhysRevC.79.049801.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  33. ^ A. Marinov; I. Rodushkin; Y. Kashiv; L. Halicz; I. Segal; A. Pape; R. V. Gentry; H. W. Miller; D. Kolb; R. Brandt (2009). "Reply to "Comment on 'Existence of long-lived isomeric states in naturally-occurring neutron-deficient Th isotopes'"". Phys. Rev. C. 79 (4): 049802. Bibcode:2009PhRvC..79d9802M. doi:10.1103/PhysRevC.79.049802.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  34. ^ J. Lachner; I. Dillmann; T. Faestermann; G. Korschinek; M. Poutivtsev; G. Rugel (2008). "Search for long-lived isomeric states in neutron-deficient thorium isotopes". Phys. Rev. C. 78 (6): 064313. arXiv:0907.0126. Bibcode:2008PhRvC..78f4313L. doi:10.1103/PhysRevC.78.064313.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  35. ^ Marinov, A.; Rodushkin, I.; Pape, A.; Kashiv, Y.; Kolb, D.; Brandt, R.; Gentry, R. V.; Miller, H. W.; Halicz, L.; Segal, I. (2009). "Existence of Long-Lived Isotopes of a Superheavy Element in Natural Au" (PDF). International Journal of Modern Physics E. 18 (3). World Scientific Publishing Company: 621–629. arXiv:nucl-ex/0702051. Bibcode:2009IJMPE..18..621M. doi:10.1142/S021830130901280X. Retrieved February 12, 2012.
  36. ^ Cwiok, S.; Heenen, P.-H.; Nazarewicz, W. (2005). "Shape coexistence and triaxiality in the superheavy nuclei". Nature. 433 (7027): 705–9. Bibcode:2005Natur.433..705C. doi:10.1038/nature03336. PMID 15716943.
  37. ^ Elert, G. "Atomic Models". The Physics Hypertextbook. Retrieved 2009-10-09.
  38. ^ Eisberg, R.; Resnick, R. (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles. Wiley.
  39. ^ Bjorken, J. D.; Drell, S. D. (1964). Relativistic Quantum Mechanics. McGraw-Hill.
  40. ^ Greiner, W.; Schramm, S. (2008). "American Journal of Physics". 76: 509. {{cite journal}}: Cite journal requires |journal= (help), and references therein

Further reading