Periodic Table Quantum Mechanics Consistent

Periodic table of the chemical elements quantum mechanics consistent

s block 0

l

Periodic table quantum mechanics consistent10 f block d block p block 3 2 1 Number of electrons in subshell 1…14 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5

2m+1 1 2 n spheri3 nodes: cal 14 nodes: 2 elements elements m=0 n

Two vibration nodes (parallels or meridians) : 10 elements per line

K 1 H L M N O P Q

2 3 4 5 6 7

Li Na K Rb Cs Fr

P 6 La Q 7 Ac

m=±1

Be Mg Ca Sc Ti V Cr Mn Fe Co Ni Sr Y Zr Nb Mo Tc Ru Rh Pd Ba 57 to 70 Lu Hf Ta W Re Os Ir Pt Ra 89 to 102 Lr Rf Db Sg Bh Hs Mt Ds

Ce Th

He B C N O F Ne Al Si P S Cl Ar Cu Zn Ga Ge As Se Br Kr Ag Cd In Sn Sb Te I Xe Au Hg Tl Pb Bi Po At Rn Uuu Uub 113 Uuq 115 Uuh 117 Uuo

Lanthanides and actinides (f bloc) 5 6 7 8 9 10 m=±1 m=±2

3

4

Pr Pa

Nd U

Pm Np

Sm Pu

Eu Am

m=±1

m=±2

He

1 2 m=0

One vibration node (parallel or meridian) : 6 elements per line m=0

m=0

6

Gd Cm

Tb Bk

Dy Cf

11

12 13 m=±3

14

Ho Es

Er Fm

Yb No

Tm Md

Abstract The official periodic table of the chemical elements is already 97 % in accord with quantum mechanics. Three elements only do not fit correctly into it, in disagreement with the Pauli exclusion principle1. It is a great simplification that gives mathematical coherence the the periodic table. A consequence is that helium should be beside hydrogen in the s-block and not in the p-block as shown in most tables. Lutetium and lawrencium pertain to the d-block of the transition metals and should not be in the f-block with the rare earths or the actinoids (actinides). By replacing the lanthanoids (rare earths or lanthanides) and actinoids boxes of the official IUPAC periodic table by those of lutetium and lawrencium, with helium placed beside hydrogen, the compact periodic table is 100 % correct according to the Schrödinger model of the hydrogen atom completed with the Pauli exclusion principle.

History of the periodic table The Mendeleev table is more than one century old. The number of columns was 6 in 1869, corrected to 8 in 1871, at the origin, based on atomic masses with twelve lines and eight columns, corresponding approximately to the s, p and d-blocks of quantum mechanics. The transition metals were moved separately and the corresponding column was replaced by the rare gases after their discovery by Ramsay. Moseley replaced the mass with the atomic number as a classification criterion. The transuranians were discovered by Seaborg who placed the lanthanoids and actinoids separately, below the table, for reasons of compactness. Various table shapes may be found in the literature. On the usual ones, one line is a period with a total of 6. Columns are grouped approximately in four blocks named s, p, d, f, respectively for the values 1, 2, 3, 4 of the second quantum number l. Each block contains theoretically an even number of elements (a consequence of the Pauli exclusion principle). They are given by the formula 2(2l + 1) e.g. 2, 6, 10, 14. On the IUPAC official table2, shown on figure 1 there are 18 columns. Columns 4 to 12 form the d-group, the transition metals, formerly part of Mendeleev group VIII. Column VIII was then used for the rare gases and renamed 18. The f-block (l = 3) is apart and contains the lanthanides and the actinides. Although updated many times, the periodic table has some anomalies shown on table below. There is a vacant box beside hydrogen and a strange discontinuity below yttrium Y.

Official periodic table (IUPAC) 1 H Li Na K Rb Cs Fr

2 ? Be Mg Ca Sr Ba Ra

3

4

Sc Y 57 to 71 ? 89 to 103 ?

9 10 11 12 13 14 15 16 17 18 He B C N O F Ne Al Si P S Cl Ar V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Db Sg Bh Hs Mt Ds Uuu Uub 113 Uuq 115 Uuh 117 Uuo Lanthanides and actinides 10 11 12 13 14 15 6 7 8 9 Lr Sm Eu Gd Tb Dy Ho Er Tm Yb Pu Am Cm Bk Cf Es Fm Md No Lu 5

Ti Zr Hf Rf

1

2

3

4

5

La Ac

Ce Th

Pr Pa

Nd U

Pm Np

6

7

8

Simplified Schrödinger equation based model We shall apply the Schrödinger model of the hydrogen atom where the electronic structure of the atoms is not taken into account. The Schrödinger equation is indeed untractable for a large number of electrons. The solution of the Schrödinger equation of the hydrogen atom is given by the orbitals defined by three quantum numbers n, corresponding to the energy, l, and m defining the spherical harmonics. It is not necessary to solve the Schrödinger equation to obtain them, simple considerations of symmetry suffice. The representation used here is a plane one showing only the nodes. The total number of nodes is given by the principal quantum number n. The simplest s state is spherical. There is only one possibility, with one node if n = 1. According to the Pauli exclusion principle, there are then two quantum states 1s1 and 1s2 that may accept one electron each corresponding to two chemical elements, hydrogen and helium. For n = 2, there are two spherical nodes 2s1 and 2s2, giving rise again to 2 elements (Li and Be). It is also possible to have one spherical node and one plane node. Assuming an axial symmetry, this node may be equatorial or meridian. The equator, being insensitive to the sense of rotation gives rise to only one mode of vibration, 2p1 and 2p2 corresponding to 2 elements (B ,C). The rotation of the meridian may be detected ; therefore, there are two modes of vibration that may be rotating clockwise or counterclockwise giving 4 quantum states 2p3, 2p4, 2p5 and 2p6. We have then four elements more. Adding all these elements we have 2 + 2 + 2 + 4 = 10 elements for the two first shells ending with Mg. It may continue similarly until Ca, but then the levels are then intermingled due to the electronic repulsion between the electrons, difficult to compute. It is then necessary to know experimentally the order of the shells and subshells : 1s-2s-2p-3s-3p4s3d-4p-5s-4d-4p-5p-6s-4f-5d-6p-7s-5f-6d. This represents the complete periodic table, indeed not very readable as such. Therefore, on the table below a graphical representation is used instead which is the above Mendeleev table slightly modified and completed with simplified drawings of the orbitals :

s block 0

l

Periodic table quantum mechanics consistent10 f block d block p block 3 2 1 Number of electrons in subshell 1…14 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5

2m+1 1 2 n spheri3 nodes: cal 14 nodes: 2 elements elements m=0 n

Two vibration nodes (parallels or meridians) : 10 elements per line

K 1 H L M N O P Q

2 3 4 5 6 7

Li Na K Rb Cs Fr

P 6 La Q 7 Ac

m=±1

Be Mg Ca Sc Ti V Cr Mn Fe Co Ni Sr Y Zr Nb Mo Tc Ru Rh Pd Ba 57 to 70 Lu Hf Ta W Re Os Ir Pt Ra 89 to 102 Lr Rf Db Sg Bh Hs Mt Ds

Ce Th

3

Pr Pa

He B C N O F Ne Al Si P S Cl Ar Cu Zn Ga Ge As Se Br Kr Ag Cd In Sn Sb Te I Xe Au Hg Tl Pb Bi Po At Rn Uuu Uub 113 Uuq 115 Uuh 117 Uuo

Lanthanides and actinides (f bloc) 4 5 6 7 8 9 10 m=±1 m=±2 Nd U

Pm Np

Sm Pu

Eu Am

m=±1

m=±2

He

1 2 m=0

One vibration node (parallel or meridian) : 6 elements per line m=0

m=0

6

Gd Cm

Tb Bk

Dy Cf

11

12 13 m=±3

14

Ho Es

Er Fm

Yb No

Tm Md

Helium It is well known that helium has a 1s2 structure, with two electrons, which is a spherical mode of vibration, the same as hydrogen 1s1, with one electron. Helium, pertaining to the s-block, is usually placed with the other rare gases in the p-block3 where the electronic structure is np6 with six electrons in the outer shells instead of two for helium. In 1962 Bartlett4 showed that the noble gases were not so inert. There exists compounds of xenon and krypton with fluor, chlorine, hydrogen, platinum4, gold5 … There is no chemical reason any more to place helium with the other noble gases6. The vacant box beside hydrogen should be filled with helium where it has its natural place, as was shown by Bohr in 19211.

Lutetium and lawrencium Lutetium and lawrencium are traditionally considered as belonging respectively to lanthanoids and actinoids having 15 elements each. According to the Pauli exclusion principle, the f-block contains an even maximum of 14 electrons. Lutetium (also named Cassiopium Cp) pertains to the d block of the transition metals1 with 10 elements and

therefore not to the f-block of the lanthanoids. Lutetium is not included in the study of the valency of rare earths by Strange et al7. According to Jensen8, physical and chemical properties unanimously favour the placement of lutetium below scandium and yttrium and not within the lanthanoids. This is also valid for the actinoids, mostly unknown at the time of Bohr. A physical or chemical classification criterion seems difficult to apply to the newly discovered actinoids that decay seconds after they are formed9.

Suggested updating of the periodic table Bent6 recommends to place helium above beryllium. The exclusion principle is then satisfied. Lutetium and lawrencium should be in the d-block below scandium and yttrium. The lanthanoids and actinoids are now 14 each for the f-block as predicted by quantum mechanics, e.g. the Schrödinger equation combined with the Pauli exclusion principle. The only unambiguous classification criterion is the electronic structure, as was put forward by Bohr and Pauli more than seventy years ago1. The drawings show the nodes of the vibration modes of the hydrogen atom according to Schrödinger. It is a simplified representation of the atomic orbitals10. It has to be distinguished from the classification based upon the electronic structure were the complicated influence of the repulsion between electrons produces irregularities. As a conclusion, the official table has only a 3 % error fraction. Just by placing adequately three elements hydrogen, lutetium and lawrencium, the Mendeleev periodic table will be 100 % correct with respect to quantum mechanics without the three strange inconsistencies it has presently.

References 1. Born M., Dougall J., Radcliffe J.M., Blin-Stoyle, R.J., Atomic Physics. Dover, New York, 1989 (first édition in 1935). 2. Holden, N.E. and Coplen Ty., The Periodic Table of the Elements. Chemistry International, 26, No. 1 January-February 2004 3. Scerri, E.R., Some aspects of the metaphysics of chemistry and the nature of the elements. HYLE. 11 (1-2), pp. 127-145, 2005. 4. Bartlett N., Xenon Hexafluoroplatinate(V) Xe+[PtF6]–. Proc. Chem. Soc. (June), 218, 1962. 5. Brisdon A.K., Halogens and Noble Gases. Annu. Rep. Prog. Chem., Sect. A, 97, 107– 116, 2001. 6. Bent, A., New Ideas in Chemistry from Fresh Energy for the Periodic Law. Authorhouse, Bloomington, IN, 2006 7. Strange, P., Svane, A., Temmerman, W. M., Szotek, Z., Winter H., Understanding the valency of rare earths from first-principles theory. Nature (London), 399, 756-758, 1999. 8. Jensen, W.B., The Positions of Lanthanum (Actinium) and Lutetium (Lawrencium) in the Periodic Table. Journal of Chemical Education, 59, p. 634-636, 1982. 9. Kendall Powell, Heavy elements: A very brief encounter. Nature, 418, 815-816, 2002. 10. Schaeffer, B., Relativités et quanta clarifiés, Publibook, Paris, 2007