The task is reduced to calculation of parameters of orbits of orbital leptons:
of radius of orbits of leptons.
of the linear and radial velocity of leptons in an orbit.
of energy of orbital leptons.
And in case of
Mesons and
a neutron,
having calculated radius of an orbit of an exterior
,
we that shall calculate their size.
1. Calculation of radius of an orbit.
In calculations, we shall proceed from the assumption that
leptons
is dotisimilar and inside of particles interreact among themselves exclusively by means
of electromagnetic and gravitational fields. And, in their classical understanding.
As is known, that one the electrically charged and possessing a rest mass particle (1),
could be in an orbit around of other similar particle (2), it is necessary,
that Coulomb and gravitational forces acting on it, have been counterpoised by a centrifugal force.
Solving this equation concerning radius of an orbit, we shall gain the general formula:
Here:
m_{1} and m_{2}
- rest masses of particles;
q_{1} and q_{2}
- electrical charges of particles;
V_{1}
- orbital linear velocity of a particle 1;
c
- velocity of light;
f
- gravitational constant;
K
- the constant equal of .
The gained formula is universal. After it it is possible to calculate radius of an orbit:
around
.
around
.
around
.
1.1 Calculation of radius of an orbit of neutrino.
In case of orbital neutrino, the right part of the formula [1.1] is equal to zero, m_{2}
is equal to a rest mass of an electron. Substituting values of a constant and a rest mass,
we shall gain the formula for radius of an orbit (in meters):
Here:
V_{1}
- orbital linear velocity of
(m/s).
1.2 Calculation of radius of an orbit of
.
In case of orbital
,
the left (gravitational) part of the formula [1.1], it is insignificantly small in comparison
with the right (Coulomb) part and it can be neglected, m_{1} is equal to a rest mass of
.
The rest mass of
depends on velocity of orbital
entering into its composition and can be within the limits of - from equal to a rest mass of an electron
(neglecting a rest mass of neutrino) up to infinitum.
What actually velocity of
into
while it is difficult to tell.
But, it is possible to tell unambiguously, that having accepted a rest mass of
to an equal rest mass of an electron, we shall gain limitation on maximum value of radius.
Having accepted the above-stated assumption, and having substituted all known values and constants
in the formula [1.1], we shall gain the formula for radius of an orbit (in meters):
Here:
V_{1}
- orbital linear velocity of
(m/s).
2. Calculation of velocity of orbital
.
To try to define velocity of an orbital
it would be reasonable, observing of process of
-decay.
In fact thus
simply goes from the orbit.
But, as is known, velocity of electrons taking off at it is different. Equally, as well as velocity
of antineutrino.
That fact, that the total of energies of an electron and antineutrino is always identical,
narrows down search a little, but does not give the unambiguous answer.
As an identical kinetic energy can have:
- and fast
,
with the slowest antineutrino "onboard",
- and slow, but massive
,
which massiveness are "increased" due to fast "onboard" antineutrino.
As the energy inside of
actually is distributed and what velocities of leptons making it, I think will explain experiment.
Or - the competent physicist with "lucid mind". :-)
Purely now our task - only to estimate some general parameters.
Therefore, considering, that an electron more than in 170000 times more massive than antineutrino,
we shall accept "determining role" electron.
Antineutrino thus fulfils some "a qualitative role", while to us is unknown.
In fact, it is easier to present itself, that at
-decay for any reason
the massive electron "is braked", but not "dispersed", and surplus of its energy is carried away
by light antineutrino. Rather the reverse...
Purely, so are appear a postulate specified last in
Basis principles.
But all of this perhaps is not true, and all - on the contrary....
In view of all aforesaid, velocity of
can be calculated under the formula:
Here:
c
- velocity of light;
E_{0}
- rest energy
;
E
- total energy
.
Substituting in the formula [2.1] value of velocity of light and accepting E_{0}
to an equal rest energy of an electron, we shall gain the second working formula, for velocity of
(in m/s):
Here:
E
- total energy
(Mev).
3. Checkout of the gained formulas.
To check up formulas it is the most convenient at calculation of an orbit of an electron in 1-st Bohr orbit
in atom of hydrogen (lowermost).
Here the electron does not have close allocated antineutrino, but nevertheless...
As is known, the kinetic energy of an electron in an orbit in atom is modulo equal to its binding energy
(ionization energy).
For 1-st Bohr orbit in atom of hydrogen:
- Ionization energy = 13,53 ev.
- Total energy of an orbital electron 0,510998902 + 0,00001353 = 0,511012432 Mev.
- Velocity of an electron under the formula [2.2] (in view of more precise values of a rest energy of an electron
0,510998902 Mev and velocities of light 2,997925*10^{8} m/s)
= 2,181554*10^{6} m/s.
- Radius of an orbit of an electron under the formula [1.3] (in view of more precise value of velocity of light)
= 5,321*10^{-11} m.
- Official value of radius of the first Bohr orbit of an electron =
5,292*10^{-11} m.
I.e. there is a hope, that applying sequentially formulas [2.2] and [1.3], we can let roughly,
but estimate parameters and lower orbits of leptons.
Note: 1. Certainly, in real particles, leptons move on orbits around of the common centres
of masses instead of how it is shown in
periodic tables.
As in particles, in difference from atoms, there is no massive kernel (exception makes only a neutron).
I.e. calculation of radiuses under the above-stated formulas - no more, than estimate.
2. Probably, would be more correct to speak not "Rest energy" and "Total energy" for formulas [2.1]
and [2.2], but "Rest mass" and "Relativistic mass", accordingly. But in fact from it the essence will not vary...
3. In the given model, concepts "Energy of a particle" and "Mass of a particle"
are completely identical.