Period 8 element

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Main article: Extended periodic table

A period 8 element is any one of 50 hypothetical chemical elements belonging to an eighth period of the periodic table of the elements. They may be referred to using IUPAC systematic element names. None of these elements have been created,[1] and it is possible that none have isotopes with stable enough nuclei to receive significant attention in the near future. It is also probable that, due to drip instabilities, only the lower period 8 elements are physically possible.

If it were possible to produce sufficient quantities of these elements that would allow the study of their chemistry, these elements may well behave very differently from those of previous periods. This is because their electronic configurations may be altered by quantum and relativistic effects. This is because the energy levels of the 5g, 6f and 7d orbitals are so close to each other that they may well exchange electrons with each other. This would result in a large number of elements in the superactinide series that would have extremely similar chemical properties that would be quite unrelated to elements of lower atomic number.

The names given to these unattested elements are all IUPAC systematic names.

Contents

[edit] History

There are currently seven periods in the periodic table of chemical elements, 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 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.[2][3] No elements in this region have been synthesized or discovered in nature.[4] While Seaborg's version of the extended period had the heavier elements following the pattern set by lighter elements, other models do not. 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 rule.[5]

Blocks of the periodic table

  s-block
  p-block
  d-block
  f-block
  g-block

(Undiscovered (theorized) elements are coloured in a lighter shade)

[edit] Aufbau principle model

This model would hold if electron configurations always followed the Aufbau principle exactly.

8 119
Uue		 120
Ubn		 121
Ubu		 122
Ubb		 123
Ubt		 124
Ubq		 125
Ubp		 126
Ubh		 127
Ubs		 128
Ubo		 129
Ube		 130
Utn		 131
Utu		 132
Utb		 133
Utt		 134
Utq		 135
Utp		 136
Uth		 137
Uts		 138
Uto		 139
Ute		 140
Uqn		 141
Uqu		 142
Uqb		 143
Uqt		 144
Uqq		 145
Uqp		 146
Uqh		 147
Uqs		 148
Uqo		 149
Uqe		 150
Upn		 151
Upu		 152
Upb		 153
Upt		 154
Upq		 155
Upp		 156
Uph		 157
Ups		 158
Upo		 159
Upe		 160
Uhn		 161
Uhu		 162
Uhb		 163
Uht		 164
Uhq		 165
Uhp		 166
Uhh		 167
Uhs		 168
Uho

[edit] Pyykkö model

Pekka Pyykkö 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.[6]
Pyykkö model. Displaced elements are in boldface.
8 119
Uue		 120
Ubn		 121
Ubu		 122
Ubb		 123
Ubt		 124
Ubq		 125
Ubp		 126
Ubh		 127
Ubs		 128
Ubo		 129
Ube		 130
Utn		 131
Utu		 132
Utb		 133
Utt		 134
Utq		 135
Utp		 136
Uth		 137
Uts		 138
Uto		 141
Uqu		 142
Uqb		 143
Uqt		 144
Uqq		 145
Uqp		 146
Uqh		 147
Uqs		 148
Uqo		 149
Uqe		 150
Upn		 151
Upu		 152
Upb		 153
Upt		 154
Upq		 155
Upp		 156
Uph		 157
Ups		 158
Upo		 159
Upe		 160
Uhn		 161
Uhu		 162
Uhb		 163
Uht		 164
Uhq		 139
Ute		 140
Uqn		 169
Uhe		 170
Usn		 171
Usu		 172
Usb
9 165
Uhp		 166
Uhh		 167
Uhs		 168
Uho

[edit] Periodic trends

Periodic trends may not continue to hold at such high atomic number, and in fact may already break down in the late seventh period. For example, chemical studies performed in 2007 strongly indicate that ununquadium possesses non-eka-lead properties and appears to behave as the first superheavy element that portrays noble-gas-like properties due to relativistic effects.[7]

[edit] Elements

Period 8 is divided into five blocks, and it is the first period that includes the g-block; however, spin-orbit coupling effects reduce the validity of the orbital approximation substantially for elements of high atomic number.[5]

[edit] s-block

The elements in the s-block of period 8 have atomic numbers 119 and 120. The necessary condition for synthesising the s-block elements of period 8, ununennium and unbinilium, is to have a sensitivity on the order of femtobarns, which is currently out of reach of even the most advanced facilities.

[edit] Attempts at synthesis

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.[8]

\,^{254}_{99}\mathrm{Es} + \,^{48}_{20}\mathrm{Ca} \to \,^{302}_{119}\mathrm{Uue} ^{*} \to \ \ no\ atoms

It is highly unlikely that this reaction will be useful given the extremely difficult task of making sufficient amounts of Es-254 to make a large enough target to increase the sensitivity of the experiment to the required level, due to the rarity of the element, and extreme rarity of the isotope.

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.[9] 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.[10]

\,^{244}_{94}\mathrm{Pu} + \,^{58}_{26}\mathrm{Fe} \to \,^{302}_{120}\mathrm{Ubn} ^{*} \to \ fission\ only

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

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

\,^{238}_{92}\mathrm{U} + \,^{64}_{28}\mathrm{Ni} \to \,^{302}_{120}\mathrm{Ubn} ^{*} \to \ fission \ only

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.

[edit] g-block

Period 8 is the first period to have g-block elements, which have atomic numbers from 121 onwards, but it is not clear when the filling of the 5g subshell ends. These elements belong to the chemical series of superactinides, characterised by the filling of the 5g and 6f subshells, and they could therefore have different chemical properties that are reminiscent of the actinides; however, the proximity of the 5g and 6f subshells and the small gap between them and the 7d and 8p subshells could lead to a large number of elements whose properties are independent of their position in the periodic table.

These elements would only be detectable if they lie near the hypothesised island of stability. The stability of these elements depends on the location of the island of stability; if the island is centred around a low Z, most superactinides would be too unstable to be detected, but if it is centred around a higher Z, there is a possibility of detecting the lower superactinides.

[edit] Attempts at synthesis

The only elements in this region of the periodic table that have had attempts to synthesise them are elements 122, 124 and 126.

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

\,^{238}_{92}\mathrm{U} + \,^{66}_{30}\mathrm{Zn} \to \,^{304}_{122}\mathrm{Ubb} ^{*} \to \ \mbox{no atoms}.

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

In 2000, the Gesellschaft für Schwerionenforschung performed a very similar experiment with much higher sensitivity:

\,^{238}_{92}\mathrm{U} + \,^{70}_{30}\mathrm{Zn} \to \,^{308}_{122}\mathrm{Ubb} ^{*} \to \ \mbox{no atoms}.

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.

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. 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.[11]

On April 24, 2008, a group led by Amnon Marinov at the Hebrew University of Jerusalem claimed to have found single atoms of unbibium in naturally occurring thorium deposits at an abundance of between 10−11 and 10−12, relative to thorium.[12] 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.[13]

A criticism of the technique, previously used in purportedly identifying lighter thorium isotopes by mass spectrometry,[14][15] was published in Physical Review C in 2008.[16] A rebuttal by the Marinov group was published in Physical Review C after the published comment.[17]

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.[18] This result throws considerable doubt on the results of the Marinov collaboration with regards to their claims of long-lived isotopes of thorium, roentgenium and unbibium.

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. 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:

\,^{238}_{92}\mathrm{U} + \,^{nat}_{32}\mathrm{Ge} \to \,^{308,310,311,312,314}\mathrm{Ubq} ^{*} \to \ fission.

The team reported that they had been able to identify compound nuclei fissioning with half-lives > 10−18 s. Although very short, the ability to measure such decays indicated a strong shell effect at Z=124. A similar phenomenon was found for Z=120 but not for Z=114.[19]

The first attempt to synthesize unbihexium was performed in 1971 by Bimbot et al. using the hot fusion reaction:

\,^{232}_{90}\mathrm{Th} + \,^{84}_{36}\mathrm{Kr} \to \,^{316}_{126}\mathrm{Ubh} ^{*} \to \ no \ atoms

A high energy alpha particle was observed and taken as possible evidence for the synthesis of unbihexium. Recent research 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. To date, no other attempt has been made to synthesize unbihexium.

All other elements in this region of the periodic table and beyond have not had any attempts to synthesise them.

[edit] Feynmanium

Untriseptium, element 137, is sometimes called feynmanium (symbol Fy) because Richard Feynman noted[20] 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.[21]

[edit] 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

v = Z \alpha c \approx \frac{Z c}{137.036}

where Z is the atomic number, and α is the fine structure constant, a measure of the strength of electromagnetic interactions.[22] 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.

[edit] The Dirac equation

The relativistic Dirac equation also 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. 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.[23]

More accurate calculations including 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.[24]

More complete analysis involving relativity shows that the contradiction this particle poses may actually occur in the hypothetical element untriennium (Z = 139; see unsolved problems in chemistry).

[edit] f-block

The relativstic and quantum effects for the electron clouds of these elements are expected to be even more sensitive than those for the g-block elements, because these elements have higher atomic number. If these elements could actually be observed, they would likely be observed to have similar chemical properties, but the effect of the closeness of the 5g and 6f (and possibly also the 7d and 8p) subshells is unclear and difficult to predict because of the relativistic and quantum effects. These orbitals, being so close in energy, may fill together all at the same time, resulting in a series of very similar elements with many barely distinguishable oxidation states. The basis of periodic trends based on electron configurations may thus no longer hold.[25]

The existence of such atoms is probably theoretically possible as the upper limit for atomic number is likely Z = 173 due to the light-speed limit,[26] after which assigning electron shells would be nonsensical and elements would only be able to exist as ions, but it is not clear if our technology will ever be enough to synthesise them.

[edit] d-block and p-block

Although element 153 would likely be taken to be the last superactinide based on previous periods, the electron configurations for later elements would likely be nothing more than mathematical extrapolation because of the extreme quantum and relativistic effects the electron clouds will experience. In the unlikely case that their chemical properties may eventually be studied, it is likely that all existing classifications will be inadequate to describe them. Due to the breakdown of periodic trends expected in this region due to the closeness of energy of the 5g, 6f, 7d and 8p orbitals and other relativistic effects, it seems likely that the properties and placement in the periodic table of these elements may be of only formal significance.[25]

[edit] Electron configurations

Leonard I. Schiff predicted the electron configurations for the period 8 elements.[27] Chemical series information is purely hypothetical and based on periodic trends which may not apply to elements this heavy.[7] Pekka Pyykkö has also predicted the electron configurations for these elements.[6] The predictions are drastically different.

Chemical element Chemical series Electron configuration
(according to Schiff)
119 Uue Ununennium Alkali metal [Uuo] 8s1
120 Ubn Unbinilium Alkaline earth metal [Uuo] 8s2
121 Ubu Unbiunium Superactinide [Uuo] 8s2 7d1
122 Ubb Unbibium Superactinide [Uuo] 8s2 7d2
123 Ubt Unbitrium Superactinide [Uuo] 8s2 7d1 5g2
124 Ubq Unbiquadium Superactinide [Uuo] 8s2 7d1 5g3
125 Ubp Unbipentium Superactinide [Uuo] 8s2 7d1 5g4
126 Ubh Unbihexium Superactinide [Uuo] 8s2 7d1 5g5
127 Ubs Unbiseptium Superactinide [Uuo] 8s2 7d1 5g6
128 Ubo Unbioctium Superactinide [Uuo] 8s2 7d1 5g7
129 Ube Unbiennium Superactinide [Uuo] 8s2 5g9
130 Utn Untrinilium Superactinide [Uuo] 8s2 7d1 5g9
131 Utu Untriunium Superactinide [Uuo] 8s2 7d1 5g10
132 Utb Untribium Superactinide [Uuo] 8s2 7d1 5g11
133 Utt Untritrium Superactinide [Uuo] 8s2 7d1 5g12
134 Utq Untriquadium Superactinide [Uuo] 8s2 7d1 5g13
135 Utp Untripentium Superactinide [Uuo] 8s2 7d1 5g14
136 Uth Untrihexium Superactinide [Uuo] 8s2 7d1 5g15
137 Uts Untriseptium Superactinide [Uuo] 8s2 7d1 5g16
138 Uto Untrioctium Superactinide [Uuo] 8s2 5g18
139 Ute Untriennium Superactinide [Uuo] 8s2 7d1 5g18
140 Uqn Unquadnilium Superactinide [Uuo] 8s2 7d1 6f1 5g18
141 Uqu Unquadunium Superactinide [Uuo] 8s2 7d1 6f2 5g18
142 Uqb Unquadbium Superactinide [Uuo] 8s2 7d1 6f3 5g18
143 Uqt Unquadtrium Superactinide [Uuo] 8s2 7d1 6f4 5g18
144 Uqq Unquadquadium Superactinide [Uuo] 8s2 6f6 5g18
145 Uqp Unquadpentium Superactinide [Uuo] 8s2 6f7 5g18
146 Uqh Unquadhexium Superactinide [Uuo] 8s2 7d1 6f7 5g18
147 Uqs Unquadseptium Superactinide [Uuo] 8s2 7d1 6f8 5g18
148 Uqo Unquadoctium Superactinide [Uuo] 8s2 6f10 5g18
149 Uqe Unquadennium Superactinide [Uuo] 8s2 6f11 5g18
150 Upn Unpentnilium Superactinide [Uuo] 8s2 6f12 5g18
151 Upu Unpentunium Superactinide [Uuo] 8s2 6f13 5g18
152 Upb Unpentbium Superactinide [Uuo] 8s2 6f14 5g18
153 Upt Unpenttrium Superactinide [Uuo] 8s2 7d1 6f14 5g18
154 Upq Unpentquadium Transition metal [Uuo] 8s2 7d2 6f14 5g18
155 Upp Unpentpentium Transition metal [Uuo] 8s2 7d3 6f14 5g18
156 Uph Unpenthexium Transition metal [Uuo] 8s2 7d4 6f14 5g18
157 Ups Unpentseptium Transition metal [Uuo] 8s2 7d5 6f14 5g18
158 Upo Unpentoctium Transition metal [Uuo] 8s2 7d6 6f14 5g18
159 Upe Unpentennium Transition metal [Uuo] 8s2 7d7 6f14 5g18
160 Uhn Unhexnilium Transition metal [Uuo] 8s2 7d8 6f14 5g18
161 Uhu Unhexunium Transition metal [Uuo] 8s1 7d10 6f14 5g18
162 Uhb Unhexbium Transition metal [Uuo] 8s2 7d10 6f14 5g18
163 Uht Unhextrium Post-transition metal [Uuo] 8s2 8p1 7d10 6f14 5g18
164 Uhq Unhexquadium Post-transition metal [Uuo] 8s2 8p2 7d10 6f14 5g18
165 Uhp Unhexpentium Post-transition metal [Uuo] 8s2 8p3 7d10 6f14 5g18
166 Uhh Unhexhexium Post-transition metal [Uuo] 8s2 8p4 7d10 6f14 5g18
167 Uhs Unhexseptium Halogen [Uuo] 8s2 8p5 7d10 6f14 5g18
168 Uho Unhexoctium Noble gas [Uuo] 8s2 8p6 7d10 6f14 5g18

[edit] See also

[edit] References

  1. ^ The heaviest element that has been created to date is ununoctium with atomic number 118, which is the last period 7 element.
  2. ^ Seaborg, Glenn (August 26, 1996). "An Early History of LBNL". http://www.lbl.gov/LBL-PID/Nobelists/Seaborg/65th-anniv/29.html. 
  3. ^ Frazier, K. (1978). "Superheavy Elements". Science News 113 (15): 236–238. doi:10.2307/3963006. JSTOR 3963006. 
  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. http://www.rsc.org/chemistryworld/News/2008/May/02050802.asp. Retrieved 2010-03-16. 
  5. ^ a b "Extended elements: new periodic table". 2010. http://www.rsc.org/Publishing/ChemScience/Volume/2010/11/Extended_elements.asp. 
  6. ^ a b 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. Bibcode 2011PCCP...13..161P. doi:10.1039/c0cp01575j. PMID 20967377. 
  7. ^ a b Gas Phase Chemistry of Superheavy Elements, lecture by Heinz W. Gäggeler, Nov. 2007. Last accessed on Dec. 12, 2008.
  8. ^ 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. http://link.aps.org/abstract/PRC/v32/p1760. 
  9. ^ THEME03-5-1004-94/2009
  10. ^ Oganessian et al.; Samanta, C.; Basu, D. (2009). "Attempt to produce element 120 in the 244Pu+58Fe reaction". Phys. Rev. C 73: 024603. arXiv:nucl-th/0507054. Bibcode 2006PhRvC..73a4612C. doi:10.1103/PhysRevC.73.014612. 
  11. ^ see Flerov lab annual reports 2000–2004 inclusive http://www1.jinr.ru/Reports/Reports_eng_arh.html
  12. ^ 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. 
  13. ^ Royal Society of Chemistry, "Heaviest element claim criticised", Chemical World.
  14. ^ A. Marinov; I. Rodushkin; Y. Kashiv; L. Halicz; I. Segal; A. Pape; R. V. Gentry; H. W. Miller; D. Kolb; R. Brandt (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. 
  15. ^ Marinov, A.; Rodushkin, I.; Kashiv, Y.; Halicz, L.; Segal, I.; Pape, A.; Gentry, R.; Miller, H. et al. (2007). "Existence of long-lived isomeric states in naturally-occurring neutron-deficient Th isotopes". Physical Review C 76 (2): 021303. arXiv:nucl-ex/0605008. Bibcode 2007PhRvC..76b1303M. doi:10.1103/PhysRevC.76.021303. 
  16. ^ 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. 
  17. ^ 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. 
  18. ^ 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. Bibcode 2008PhRvC..78f4313L. doi:10.1103/PhysRevC.78.064313. 
  19. ^ http://hal.archives-ouvertes.fr/docs/00/12/91/31/PDF/WAPHE06_EPJ_preprint1.pdf
  20. ^ G. Elert. "Atomic Models". The Physics Hypertextbook. http://physics.info/atomic-models/. Retrieved 2009-10-09. 
  21. ^ See Extended periodic table.
  22. ^ See for example R. Eisberg, R. Resnick (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles. Wiley. 
  23. ^ J.D. Bjorken, S.D. Drell (1964). Relativistic Quantum Mechanics. McGraw-Hill. 
  24. ^ W. Greiner, S. Schramm (2008). American Journal of Physics. 76. pp. 509. , and references therein.
  25. ^ a b Seaborg (ca. 2006). "transuranium element (chemical element)". Encyclopædia Britannica. http://www.britannica.com/EBchecked/topic/603220/transuranium-element. Retrieved 2010-03-16. 
  26. ^ Walter Greiner and Stefan Schramm (2008). "Resource Letter QEDV-1: The QED vacuum". American Journal of Physics 76 (6): 509. Bibcode 2008AmJPh..76..509G. doi:10.1119/1.2820395. , and references therein.
  27. ^ Leonard I. Schiff; Quantum Mechanics, third edition, p. 428, McGraw-Hill, Inc., New York, 1968.
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