8. Atoms
8.1
Introduction ....................................................................................................................... 47
8.2. Newton
and the motion of celestial bodies ...................................................................... 48
8.3. The
Bohr atom. ................................................................................................................ 49
8.4 Heisenberg’s uncertainty principle and Bohr atomic model ............................................. 51
8.5 Hydrogen atom and the Pauli exclusion principle ............................................................ 53
8.6 Helium atom ..................................................................................................................... 54
8.7 Configuration and electron orbits ......................................................................................54
8.8 Classical corrections on the Bohr magneton ................................................................... 57
8.9 Rotations of the electron. ................................................................................................ 59
8.10 Conclusion ..................................................................................................................... 60
In this section we will be completing
the Bohr’s atomic model by using the equality in the Heisenberg’s uncertainty
principle in a way in which the linear momentum and the electron orbital are
perfectly determined in the simple atoms such as hydrogen and helium.
In the same way, the
Heisenberg’s uncertainty principle determines the number of existing electrons
in each shell and subshell.
8.1 Introduction
The equation x² + y² + z² = r³ is
corresponding to
the ratio circumference r centered at the origin.
The circumference is the geometric
position of the points of the plane which are equidistant to a fix point called
center.
Figure 8.1 Circumference centered at
the origin
If we do for instance
r=1, we can know the distance from each point to the center but we do not know
the values of x e y. If we want to know the value of x e y of the figure, we
need the measure them in a way.
Figure 8.2 Uniform
circular motion
If the point
P moves at speed v (Figure 8.2)
throughout the circumference, the values of x e y are given by the following
equations.
r = r cos 𝞿 y = r sin 𝞿
|
(8.1)
|
The coordinates x e
y vary with the time but r
remains constant.
In this
section we will suppose that the electron in hydrogen atom draws a circle orbit
around the proton. In those conditions, all the intervening constants can be calculated.
The ratio of the orbit can also be calculated. The only thing that cannot be
calculated are the coordinates x e y, as there is no physic equation which
depends upon time.
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8.10 Conclusion
Obviously the QM works
since it is based on the observed particle properties observed and
consequently, it cannot deduce the particles properties.
The electron in the
hydrogen atom is at the discrete state of minimum energy, thus it cannot emit
energy.
The QM is neither
capable of explaining why the constants have the value they have.
“I still believe
in the possibility of a model of reality, that is to say, of a theory that
represents things themselves and not merely the probability of their
occurrence”.
Albert Einstein
The model of the
Universe formed by Planck spheres of four dimensions, explains the particle
properties and it also allows us to calculate them. Moreover, it allows us to
calculate the constants used by the QM and deduce the equation that the QM is
incapable of deducing.
Ultimately, an electron
has an orbit and position even though position and linear momentum cannot be
simultaneously measured. This is one of the limitations imposed by the
Universe, since the product of the position multiplied by the linear momentum
results always in an integer0. multiple of the Planck reduced constant.
The electrons spin around
the nucleus on a sphere surface, if the electric moment coincides with the
angular momentum or shape elliptic orbits on the contrary. The different number
combinations of both angular momentum, according to the number of the shell,
give rise to the number of electrons per shell taking also into account the two
possible electron spins.
As for the electron
magnetic moment, this one matches with an extraordinary accuracy with the one
experimentally measured. And there is no need to attach the electromagnetic
field by an infinite series of fine structure constant powers as proposed by
Foldy, to obtain the electromagnetic properties of the fermions. The
calculation of each of the coefficient is very laborious.
As far as I know, the
electron magnetic field has not been measured, as opposed to its magnetic
moment which has, and according to the QM is another intrinsic property of the
mass. If the electron is a rest point with electric charge, it should not have
a magnetic moment as the moment is due to the mass movement (angular momentum)
or due to the electric charge in movement (magnetic moment).
The electron is a
Planck atom with a tendency to the minimum energy state but keeping the angular
momentum ħ , hence, it cannot radiate electromagnetic energy even if it is
in a speed up moment, like in the circle movement. To radiate energy, its
energy must be higher to the minimum or its angular momentum a integer multiple
of ħ, as all particles have a minimum angular momentum ħ .
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