4d mendel english

To the Problem
of Four-Dimensional Symmetries
of the Properties of Chemical Elements
and the Interpretation of this Phenomenon
• Y.Magarshak, J.Malinsky; A three-dimensional periodic table,
Nature, vol.360, 114-115 (1992)
• Y.Magarshak, To the Problem of Four-Dimensional Symmetries in
the Properties of Chemical Elements; Scientific Israel – Technological
Advances J., vol. 6, 24-31 (2005).
• Y.Magarshak, Chemical Numbers and Quantum Numbers, Biophizika
(2005). To appear

Орбитальное Рис. 1
Квантовое Порядок заполнения оболочек
число
Порядок
заполнения
термов (подоболочек)
14F
10D
6P
2S
1 2 3 4 5 6 7 8 Главное
квантовое
число
),()( ϕθlmYrR=Ψ
[ ] 0)(
2
2
=Ψ−+∆Ψ rUE
m


EMPIRIC HUND RULE: Electronic configuration, which has
the the largest (for that electronic configuration) spin value
and the greatest possible at this value of the spin orbinal momentum
has the lowest energy.
***
Experimentally proven order of atomic orbitals energy encrease:
1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f <5d <6p <7s <5f <6d <7p < 8s

5f < 6d < 7p < 8s …
4f < 5d < 6p < 7s <
4d < 5p < 6s <
3d < 4p < 5s <
3p < 4s <
2p < 3s <
2s <
1s <

5g 6F 7D 8P 8s
5f 6d 7p 8s
Восьмой уровень
Четвертый
суперцикл
4f (14 элементов) 5d (10 элементов) 6p (6 элементов) 7s (2 элемента)
Седьмой уровень
4d (10 элементов) 5p (6 элементов) 6s (2 элемента)
Шестой уровень
Третий
суперцикл 3d (10 элементов) 4p(6 элементов) 5s (2 элемента)
Пятый уровень
3p (6 элементов) 4s (2 элемента)
Четвертый уровень
Второй
суперцикл
2p (6 элементов) 3s (2 элемента)
Третий уровень
2s (2 элемента)
Второй уровень
Первый
суперцикл
1s (2 элемента)
Первый уровень
Рис. 2
Copiright Yuri Magarshak
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8s
7S
6 S 7P
5S 6P
4 S 5P 6D
3 S 4P 5D
2S 3P 4D 5F
1S 2P 3D 4F
1 2 3 4 5 6 7 8 Level

8S
7S
6S 7P
5S 6P
4S 5P 6D
3S 4P 5D
2S 3P 4D 5F
1S 2P 3D 4F
1 2 3 4 5 6 7 8 Level

8s
7s
6s 7p
5s 6p
4s 5p 6d
3s 4p 5d
2s 3p 4d 5f
1s 2p 3d 4f
1 2 3 4 5 6 7 8 Level

Fig. 7б
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Fr Rb Na H
Ti Ga B
Lu Sc
La
Uut
Lr
Ac
Y
Al
Cs
In
K Li

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Fr Rb Na H
Ti Ga B
Lu Sc
La
Uut
Lr
Ac
Y
Al
Cs
In
K Li

(1s)2
<
(2s)2
<
(2p)6
< (3s)2
<
(3p)6
< (4s)2
<
(3d)10
< (4p)6
< (5s)2
<
(4d)10
< (5p)6
< (6s)2
<
(4f)14
< (5d)10
< (6p)6
< (7s)2
<
(5f)14
< (6d)10
< (7p)6
< (8s)2

The Basic Features
of the 4- Dimensional Pyramid
of Periodically Repeating Properties of Chemical
Elements
All chemical elements can be subdivided by
• Eight cycles having 2,2; 8,8;18,18, 32, 32
elements each
• Four Supercycles having 4, 16, 36 и 64
elements each
• Two clusters: M-cluster and F-cluster
• Paired clusters, cycles, subshells and
elements

Рис. 9a
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Порядок
термов
элементами
Порядок Порядок
заполнения заполнения
периодов 3-7 периодов 2 и 3
термам термами
Li HNaKCs RbFr
Al BGaIn
Y ScLuLr
TiUut
LaAc

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Порядок
термов
Порядок
заполнения Циклы
термов
каждого цикла
Li HNaKCs RbFr
Al BGaIn
Y ScLuLr
TiUut
LaAc

8S
7S
6S 7P
5S 6P
4S 5P 6F
3S 4P 5D
2S 3P 4D 5F
1S 2P 3D 4F
1 2 3 4 5 6 7 8 Level

n (principal quantum number)
8S
7S
6S 7P
5S 6P
4S 5P 6F
3S 4P 5D
2S 3P 4D 5F CYCLE
1S 2P 3D 4F CYCLE
1 2 3 4 5 6 7 8 Level
l (orbital quantum number)

RaSr BaMg CaHe Be
Uub
HgCdZn
UuoRuXeCrAr
Ne
Yb No
O

СHEMISTRY NUMBERS. Each chemical element can be
characterized by the set of four chemical numbers.
CLUSTER NUMBER , having one of two values: either M or F
SUPERCYCLE NUMBER (or, in short, super-number) , which
determines to which pyramid super-level element belongs and on
which super-cycle is disposed ( = 1, 2, 3, 4).
LAYER NUMBER  which determines the layer number of the
cycle in which subshell  is disposed.  has integer values from -1
(bottom layer, which in the cycle is filled first) to 0 (surface layer,
щелочные и щелочноземельные металлы, подоболочки которых
заполняются в циклах последними).
NODE NUMBER , which enumerates 2(2  + 1) elements of the
subslell.
CERTAINITY PRICIPLE: TWO CHEMICAL
ELEMENTS CAN NOT HAVE FOUR
IDENTICAL CHEMICAL NUMBERS

),()( ϕθlmYrR=Ψ
[ ] 0)(
2
2
=Ψ−+∆Ψ rUE
m

lm
l
x
mml
ml
xP
mP
ml
mll
mP
ml
mll
m
m
m
l
m
j
m
j
,...,2,1,0
;,...,2,1,0
)1(
!)!(
)!(
2
1
)(
cos)(cos
)!(2
)!(12
sin)(cos
)!(2
)!(12
2/2
=
=
−
−
+
=
+
−+
+
−+
ϕϑ
π
ϕϑ
π

0
2)1(2
222
2
=





++
+
−+ R
r
E
m
R
r
ll
dr
dR
rdr
Rd α

1
2 22
2
−−=
−=
lnn
n
m
E
r

α
where n – radial quantum number, equal to the number of
nonzero nodes of the radial part of the wave function at
finite non-zero r.

Identity of the structure of the M-cluster (as well as that of
the F-clusterl) with the dependence of n(l) for hydrogen
atom, наводят на мысль о том, that D symmetry of the
periodic elements properties on the charge of the nuclei all
elements can be considered as the sates of the single
particles.
However the necessity
a) Getting two grids, which are rotated relative to each
other by /4;
б) filling the nodes on the slide 1 (hydrogen atom) and
slide 2 (for the set of all chemical elements)in opposite
directions, and
c) The presence of paired cycles, supercycles and clusters
in periodically repeating elements properties

Орбитальное Орбитальное
квантовое квантовое
число число
(f )7
(f )7
(d )5
(d )5
(p )3
(p )3
(s )1
(s )1
Главное ПОЛУОБОЛОЧКИ ПОЛУОБОЛОЧКИ Главное
квантовое СО СПИНОМ  СО СПИНОМ  квантовое
число число
Рис.1
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