Atom

Solid consists of some atoms, each of which consists of one nucleus and some electrons. All electrons attributing to one neutral atom interact electrostatically with the nucleus. Some electrons among them can interact with electrons in another atom. The latter interaction contributes to the aggregation of atoms.

This section describes the electron configuration of atom through examining both electrostatic and electromagnetic interactions occurring on an atom. Pauli exclusion rule and Hunt's rule may be easily derived through examining these two kinds of interaction.

An atom has Z electrons and one nucleus with the positive electric charge Ze(Z: atomic number, e: electron charge). These electrons in the atom turn around the nucleus along the orbit called an atomic orbital. These electrons are called shell electrons.

The orbit of revolution of electron is defined through examining quantum-mechanically both the kinetic motion and the electrostatic interaction with the positive electric charge of the nucleus. The atomic orbital is always characterized geometrically with the following three kinds of quantum numbers: principle quantum number N, azymuthal quantum number L and magnetic quantum number M. The value of L is constrained by N and the value of M is by L (L: one of 0,1,2,3..(N-1) ) (M: one of -L,-(L-1),..0.,,(L-1),L ). The principle quantum numbers 1, 2, 3, 4, 5, 6 can be represented by K,L,M,N,O,P, respectivelyly. Each atomic orbital is defined by use of these three numbers. For example, the atomic orbital 2p1 indicates the orbital defined by principle quantum number 2, azymuthal quantum number 1 and the magnetic quantum number 1(underscript 1).
All orbitals defined by N ( different on azymuthal and magnetic quantum number, respectively) are theoretically at the same energy level as EN.

All shell electrons of atom are accommodated by some atomic orbitals. But, we must remark that the properties of orbital, defined by use of the classical Schrodinger equation, does not correctly represent the properties of atomic orbital occupied by electron.
These above orbitals is determined without taking into accout of the electromagnetic field dependent on the kinds of revolutions( clockwise or anti-clockwise). The circuit with the clockwise revolution is electromagnetically different from the other anti-clockwise circuit.
Then, the physical characteristics of orbital, defined by use of the equation only, does not correctly represent the physical characteristics of the orbital occupied by electron,

Classical Schrodinger's equation of an atom regards both clockwise and anti-clockwise momentum as the same quantity.

This constrained viewpoint is caused by Heisenberg's uncertainty rule, which means that it is impossible to determine both energy E and time t of particle simultaneously.

Et > h

The direction of the revolution of electron is determined by taking into account of time-axis.
Therefore, it is very hard to find in the classical Schrodinger solution the direction of the revolution. Neglecting time-axis, we regard both kinds of revolutions (clockwise and anti-clockwise) as the same orbital.

As one convenient method to avoid from the above constraint brought about by Heisenberg's rule, we would imagine the method to substitute the problem of the momentum direction described above for it of the self-rotation. The substitution indicates that spin(eigen-angular momentum) is independent from the angular momentum dependent on space.
However, it is never allowable to apply this substitution method to an atom system including the electromagnetic field, because of the above reason. If we applied the method to some heavy atom system, we would meet with the difficulty to inpterpret the reason why these atoms have the higher magnetic-susceptibility than light atoms.

We must remark that the sign of the magnetic quantum number is defined through examining geometrically the absolute angular momentum of electron on atomic orbital. The magnetic quantum number means the geometrical parameter to define the geometrical area made by momentum*radius. If we see the orbital by use of the polar coordinate axes(r,f,and j) the principle quantum number, the azymuthal quantum number and the magnetic quantum number may are obtained through quantum-mechanical examinations about r, f,and j, respectively. Both signs of magnetic quantum number corresponds to both positive and negative signs of the inclined angle against the standard plane, respectively ( -90 <= angle <= 90 degree).
We know that p-1, p0 and p1 , deduced by the Schrodinger's equation are different from experimental px,py and pz occupied by electron, respectively. We must remark that the former orbitals are determined without taking into account of the revolution-direction. and that the latter p orbitals, occupied by electron, are configurated so that these mutual electro-magnetic interactions may be reduced. The above discussions suggest explicitly that the difference is caused by the mutual electro-magnetic interaction.
I do not like some magic explanations so much, which means that an orbital occupied by electron is given by examinig the wavefunction-phases of these orbitals unoccupied by electron.

Please send me any suggestions and comments, if you find any practical viewpoints. Your comments will be adopted in this Page as possible as I can.Next:

See you again next time. You will see the detailed electron configurations of each atom at the next page.