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

),()( lmYrR

0)(2

2 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 All rights reserved

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


Fr Rb Na H

Ti Ga B

Lu Sc

La

Uut

Lr

Ac

Y

Al

Cs

In

K Li


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


Порядок заполнения термов

элементами

Порядок Порядок заполнения заполнения периодов 3-7 периодов 2 и 3

термам термами

Li

H

Na

K

Cs

Rb

Fr

Al

B

Ga

In

Y

Sc

Lu

Lr

Ti

Uut

La

Ac

Рис. 5




Порядок заполнения Циклы термов

каждого цикла

Li

H

Na

K

Cs

Rb

Fr

Al

B

Ga

In

Y

Sc

Lu

Lr

Ti

Uut

La

Ac

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

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

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)



Порядок Порядок заполнения заполнения периодов 3-7 периодов 2 и 3

термами термами


Li

H

Na

K

Cs

Rb

Fr

Al

B

Ga

In

Y

Sc

Lu

Lr

Ti

Uut

La

Ac

Ra Sr Ba Mg Ca He Be

Uub Hg Cd Zn

Uuo Ru Xe Cr Ar 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

),()( lmYrR

0)(2

2 rUE

m

lm

l

xmml

mlxP

mPml

mll

mPml

mll

mm

ml

mj

mj

,...,2,1,0

;,...,2,1,0

)1(!)!(

)!(

2

1)(

cos)(cos)!(2

)!(12

sin)(cos)!(2

)!(12

2/2

02)1(2

222

2

R

rE

mR

r

ll

dr

dR

rdr

Rd

1

2 22

2

lnn

n

mE

r

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

makes the derivation of the equation, which solution possess the needed properties, highly nontrivial.

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


Рис. 4


1s 2s 3s 4s 5s 6s 7s 8s 1s 2s 3s 4s 5s 6s 7s 8s

2p 3p 4p 5p

3d 4d 5d 7d

4p 5p 6p 7p

3d 4d 5d 6d

4F 5F

2p 3p 6p 7p

4f 5f

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