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, mL, mS)
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
|
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 (EK)
is the sum of rotation and vibration; EK
= E1 + E2 = (q2
+ 2q + ½)E0
A potential energy (V) is; V
= -qE0
Total energy (ET) is; ET
= EK + 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.