The Janet Periodic Table (aka Left Step Table) may be re-arranged as a series of square matrices. Each element is represented as a cell and is identified by the atomic number (Z), shown as the upper number 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) as shown below;

Matrix; a = 1

2 1s	1 1s
4 2s	3 2s

 

Matrix; a = 2

9 2p	8 2p	5 2p	6 2p
10 2p	12 3s	11 3s	7 2p
18 3p	20 4s	19 4s	15 3p
17 3p	16 3p	13 3p	14 3p

 

Matrix; a = 3

28 3d	27 3d	26 3d	21 3d	22 3d	23 3d
29 3d	35 4p	34 4p	31 4p	32 4p	24 3d
30 3d	36 4p	38 5s	37 5s	33 4p	25 3d
48 4d	54 5p	56 6s	55 6s	51 5p	43 4d
47 4d	53 5p	52 5p	49 5p	50 5p	42 4d
46 4d	45 4d	44 4d	39 4d	40 4d	41 4d

 

Matrix; a = 4 

67 4f	66 4f	65 4f	64 4f	57 4f	58 4f	59 4f	60 4f
68 4f	78 5d	77 5d	76 5d	71 5d	72 5d	73 5d	61 4f
69 4f	79 5d	85 6p	84 6p	81 6p	82 6p	74 5d	62 4f
70 4f	80 5d	86 6p	88 7s	87 7s	83 6p	75 5d	63 4f
102 5f	112 6d	118 7p	120 8s	119 8s	115 7p	107 6d	95 5f
101 5f	111 6d	117 7p	116 7p	113 7p	114 7p	106 6d	94 5f
100 5f	110 6d	109 6d	108 6d	103 6d	104 6d	105 6d	93 5f
99 5f	98 5f	97 5f	96 5f	89 5f	90 5f	91 5f	92 5f

 

Location of Elements; 

Each matrix is identified by “a” ; a = 1,2,3,4

The upper half of each matrix is identified by; m_n =  +½

The lower half of each matrix is identified by; m_n =  -½

The right half of each matrix is identified by; m_S =  +½

The left half of each matrix is identified by; m_S =  -½

A matrix may be viewed as a 2x2 core surrounded by concentric square rings.

The core of each matrix is identified as; l = 0

The outermost ring of each matrix is identified as; l = a - 1

Where;  l = (0,1,2,3) = (s,p,d,f)

Any cell located on a major diagonal of a matrix is identified as; m_L = 0.  A column displacement from the diagonal is defined as m_L > 0.  A row displacement from the diagonal is defined as m_L < 0

If an element is represented by an atomic number (Z) the location of the element is a sum of three determinants (D₁,D₂,D₃).           Z = D₁ + D₂ + D₃ 

The Matrix Periodic Table; 

The Matrix Periodic Table may have each element represented by chemical symbol as follows;

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

 

For further information please see;  

 
                        http://quantumdeterminants.blogspot.ca/ 

http://periodicslicing.blogspot.ca/