The Janet Periodic Table (Left Step Table) may be re-arranged as a series of square matrices. Each element is represented as a cell, and is identified as the upper symbol of each cell. The quantum numbers (n, l, m_L, m_S) determine the location of an element within the table. The quantum pair (n, l ) are the lower numbers in each cell. Four matrices are required, each matrix is identified by a “matrix number” (a).

A 3D periodic table may be created if each cell is changed to a cubic block, and the matrices are stacked vertically. Matrix01 (a=1) is the top level and Matrix04 is the base. The resulting 3D P.T. resembles a stepped pyramid.

Vertical slices reveal interesting vertical relationships between the elements. Each slice has two views (sections). Major slicing gives eight sections; four orthogonal sections (two major orthogonal slices) and four diagonal sections. Major slicing reveals all four “levels” of the P.T. Minor slicing (orthogonal and diagonal) also reveals local relationships. Minor slicing does not account for all levels. Two major slices are shown below;

Major Orthogonal Slice (“North” View);

			He 1s	H 1s
		Ne 2p	Mg 3s	Na 3s	N 2p
	Zn 3d	Kr 4p	Sr 5s	Rb 5s	As 4p	Mn 3d
Yb 4f	Hg 5d	Rn 6p	Ra 7s	Fr 7s	Bi 6p	Re 5d	Eu 4f

 

Major Diagonal Slice (“North-West” View);

			Be 2s	H 1s
		Cl 3p	Ca 4s	Na 3s	C 2p
	Pd 4d	I 5p	Ba 6s	Rb 5s	Ge 4p	V 3d
Es 5f	Ds 6d	117 7p	120 8s	Fr 7s	Pb 6p	Ta 5d	Nd 4f

 

The four matrices are;

Matrix; a = 1

He 1s	H 1s
Be 2s	Li 2s

 

Matrix; a = 2

F 2p	O 2p	B 2p	C 2p
Ne 2p	Mg 3s	Na 3s	N 2p
Ar 3p	Ca 4s	K 4s	P 3p
Cl 3p	S 3p	Al 3p	Si 3p

 

Matrix; a = 3

Ni 3d	Co 3d	Fe 3d	Sc 3d	Ti 3d	V 3d
Cu 3d	Br 4p	Se 4p	Ga 4p	Ge 4p	Cr 3d
Zn 3d	Kr 4p	Sr 5s	Rb 5s	As 4p	Mn 3d
Cd 4d	Xe 5p	Ba 6s	Cs 6s	Sb 5p	Tc 4d
Ag 4d	I 5p	Te 5p	In 5p	Sn 5p	Mo 4d
Pd 4d	Rh 4d	Ru 4d	Y 4d	Zr 4d	Nb 4d

 

Matrix; a = 4 

Ho 4f	Dy 4f	Tb 4f	Gd 4f	La 4f	Ce 4f	Pr 4f	Nd 4f
Dr 4f	Pt 5d	Ir 5d	Os 5d	Lu 5d	Hf 5d	Ta 5d	Pm 4f
Tm 4f	Au 5d	At 6p	Po 6p	Tl 6p	Pb 6p	W 5d	Sm 4f
Yb 4f	Hg 5d	Rn 6p	Ra 7s	Fr 7s	Bi 6p	Re 5d	Eu 4f
No 5f	112 6d	118 7p	120 8s	119 8s	115 7p	Bh 6d	Am 5f
Md 5f	111 6d	117 7p	116 7p	113 7p	114 7p	Sg 6d	Pu 5f
Fm 5f	Ds 6d	Mt 6d	Hs 6d	Lr 6d	Rf 6d	Db 6d	Np 5f
Es 5f	Cf 5f	Bk 5f	Cm 5f	Ac 5f	Th 5f	Pa 5f	U 5f

Generic Quantum Energies;

Let a generic quantum number (q) be associated with a quantum angle (γ);   q = (q+1)Tan(½γ)

A generic quantum energy of rotation (E₁) is;      E₁ = q(q+1)E₀

A generic quantum energy of vibration (E₂) is;    E₂ = (q+½)E₀

Where; q(q+1) = (q+½)Tan(γ)

                E₀ is a fundamental energy

A kinetic energy (E_K) is the sum of rotation and vibration;   E_K = E₁ + E₂  = (q² + 2q + ½)E₀ 

A potential energy (V) is;                                   V = -qE₀ 

Total energy (E_T) is;                                             E_T = E_K + V  = (q² + q + ½)E₀ 

q(q+1) = (q² + q + ½)Sin(γ)

(q+½) = (q² + q + ½)Cos(γ)

Conclusion;

The Left Step Periodic Table may be manipulated into a series of four square matrices, which in turn may be converted into a 3D Periodic Table resembling a stepped pyramid. The location of any element is determined by three determinates which are composed of quantum numbers. Various “vertical slices” (major and minor) through the “pyramid” will give sections (views) which reveal interesting vertical relationships between the elements.

Web blogs;  http://quantumdeterminants.blogspot.ca/ 

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