_{1}

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Based on the regular polyhedron model of multi-electronic atom combined with the Bohr hypothesis, the following supposition is put forward: the electron momentum multiplied by the inscribed sphere radius of edges of each regular polyhedron is equal to the Planck constant. The relationship between saturation magnetization rates and Planck constants is determined, and the ferromagnetism of atoms is obtained from regular dodecahedron and regular hexahedron. Then, terbium, dysprosium, and holmium saturation magnetization rate are obtained from electronic regular polyhedron configuration. Derivation of matter wave formula is from thermodynamics, avoiding over speed of light.

Niels Bohr presented three assumptions in 1913: steady state assumption, quantized track hypothesis, and Bohr frequency condition [

Page 7 of literature [

In this study,

Formula (13) on page 6 of literature [

Formula (2) on page 3 of literature [

For regular dodecahedron, a is the edge length of regular dodecahedron, which is the side length of regular pentagon:

By using Formula (1) to Formula (5) in this paper, the following is obtained:

For regular hexahedron, a is the edge length of regular hexahedron, which is the side length of square:

For regular hexahedron (see

By using Formulas (1), (3), (7), (8), and (9), the following is obtained:

The following is presented from Formula (6):

where

Page 18 of literature [

According to Section 26.3 of literature [

By using Formula (11) to Formula (14), the theoretical value of

The electronic configuration of terbium is 2, 8, 12, 6, 12, 6, 12, 4, 3. Three regular dodecahedrons and two regular hexahedrons exist, and the magnetic moment of each atom is

By using Formulas (11) to (14) and Formula (16), the theoretical value of

In addition, the electron shell of iron only has one regular dodecahedron. By using Formula (12) and Formula (14), the theoretical value of

The comparison of the value of each theory value and the above experimental value indicates that the difference is small. If the paramagnetic or diamagnetic effect of other electron shell is considered, error will be smaller.

In Bohr Theory, the quantum number of each electron shell is increasing,

From the formula of thermodynamics,

See page 10 of literature [

From the above two formula, get

For multi shell of electrons, s is the number of shell, the energy

Electronic is a wave, also

Resonance condition

When the number of electron shell is equal to the number of the main quantum number,

The numerical range of degrees of freedom:

In the regular polyhedron, the inscribed circle of regular polygon of edges is the electronic orbit. The radius of inscribed sphere of edges is the distance of edges to the center and is the electrons to the nucleus distances but not electronic circular motion radius. By assuming that the electron momentum multiplied by the inscribed sphere radius of edges of each regular polyhedron is equal to the Planck constant, the relationship between the saturation magnetization rates and Planck constants is obtained. The ferromagnetism of atoms is from regular dodecahedron and regular hexahedron. Then, according to the electronic regular polyhedron configuration, ter- bium, dysprosium, and holmium saturation magnetization rate are obtained. Matter wave formula can be derived from the thermodynamics.

ZilongKong, (2015) Ferromagnetic Calculation of Terbium Dysprosium and Holmium with Polyhedron Electron Shell. Journal of Modern Physics,06,1776-1780. doi: 10.4236/jmp.2015.613179