Top page ( correct Bohr model )

New Bohr model carbon, hydrogen bonds.

de Broglie wavelength determines all structures.

*(Fig.1) Eight valence electrons = regular hexahedron.*

Neon is stable noble gas, and has **eight** valence electrons in **n = 2** orbitals.

Considering **symmetric** distribution due to repulsive Coulomb forces, regular hexahedron is natural.

In Bohr-Sommerfeld model, principal quantum number, n = 2 means **2 ×** *de Broglie* wavelength orbits.

*(Fig.2) 2 × de Broglie wavelength orbits. Each is a pair of opposite phases.*

As shown in Davisson-Germer experiment, each de Broglie wavelength consists of a **pair** of ± phases, which are **opposite** and cancel each other.

**2** × de Broglie wavelength orbits can contain **2** electrons, as shown in Fig.2.

There are 4 *midpoints* (= **2** midlines ) with **zero** phases between ±phases.

*(Fig.3) Electron 1 (= e1 ) orbit with 2 electrons.*

Fig.3 is "e1" orbit containing **two** electrons on the **opposite** sides.

This orbit is supposed to be a little elliptical **intersecting** hexahedron at 4 vertices.

*(Fig.4) Electron 2 (= e2 ) orbit "perpendicular" to e1 orbit.*

As shown in Fig.4, e2 orbit with 2 electrons crosses e1 orbit **perpendicularly** at **2** points.

"Perpendicular crossing" is important for **avoiding** destructive interference.

*(Fig.5) Electron (= e3 ) orbit with 2 electrons.*

*(Fig.6) Electron 4 (= e4 ) orbit "perpendicular" to e3 orbit.*

In the same way, e4 orbit crosses e3 orbit **perpendicularly** at **2** points.

Each orbit contains **two** electrons.

*(Fig.7) "e1" and "e3" orbits cross perpendicularly, too.*

As shown in Fig.7, "**e1**" and "**e3**" ( and "e2" and "e4" ) orbits cross **perpendicularly** at 2 points.

This is the **same** mechanism as Bohr model helium.

*(Fig.8) Starting positions in 4 orbits. *

We choose Fig.8 as starting electrons' positions in 4 orbits.

"e2" (or "e4" ) electrons cross "e1" ( or "e3" ) orbit **perpendicularly**, *avoiding* destructive interference.

*(Fig.9) Each electron can avoid other electrons' de Broglie "annoying" phases.*

Fig.9 is from the viewpoint of "**e1**" orbit which *e2* orbit crosses **perpendicularly**.

As shown in Fig.10, 2 × de Broglie wavelength orbit contains **2** **midpoint** lines with **zero** phase.

Each of this **2** × "*midpoint*" lines contain "e3" ( or "e4" ) orbit.

So, total number of Ne orbits is "**4**" (= "*e1*", "*e2* = perpendicular", "*e3, e4* = midpoint lines").

*(Fig.10) Midpoints = "Zero" phases have NO influence on other de Broglie waves.*

Due to "**zero**" phases of midpoint, "*e3*" and "*e4*" orbits can **avoid** the **bad** influences of "**e1**" wave phases. So each electron can move **independently** from other de Broglie waves, which means **stable**.

*(Fig.11) Each electron can move independently from other "annoying" phases.*

Fig.11 shows the periodic movements of all **eight** electrons in Bohr model Neon.

Electrons can move smoothly, **NOT** crashing into other electrons.

*(Fig.12) Electrons always cross other "opposite" wave phases, "neutralizing" total phases.*

As seen in Fig.11 and Fig.12, each electron can *cross* other electrons' orbits **perpendicularly**, when they are **opposite** wave phases to each other.

"Perpendicular crossing" means each de Broglie wave can **avoid** destructive interference.

And crossing of "**opposite**" wave phases can **neutralize** total wave phases at all points ( ±phases = zero ).

"**Neutralization**" of wave phases means any other electrons can be **free** from other wave ( bad ) influences, and move stably and **independently**, NOT to be disturbed. See also this page.

*(Fig.13) Next regular icosahedron cannot make orbits perpendicular to each other.*

Next regular polyhedron is regular icosahedron with **12** vertices.

But as shown in Fig.13, each electron in this icosahedron **cannot** cross other orbits perpendicularly.

Furthermore, 6→6' orbit is *independent* from other orbtis, meaning "**asymmetric**".

So, this regular icosahedron structure is **unstable** for electron's movement.

*(Fig.14) The change of the first ionization energy shows us de Broglie wavelength. *

When we look at the change of the first ionization energies of atoms, we can find **where** the orbital de Broglie wavelengths change.

For example, in the periodic table ( see this, this ), the first ionization energies suddenly **decreases** in He → Li (= 24.6 eV → 5.4 eV ), and Ne → Na ( 21.6 eV → 5.1 eV ) transitions.

**Sudden drop** in the ionization energies means **de Broglie** wavelengths (= orbital *radius* ) **increases** by one at these points.

*(Fig.15) 2 × 4 orbits make stable regular hexahedron in Ar.*

When we see the sudden drop in the first ionization energies from Ar to K ( **15.8** eV → **4.3** eV ), we can understand the orbits of **3** × de Broglie wavelengths **end** at Ar.

So from **K** (= potassium ), **4** × de Broglie wavelength orbits start.

Though 3 × de Broglie wavelengths contain total 3 electrons in each orbit, 2 × 4 orbits (= total 8 electrons ) can form **stable** regular *hexahedron* like Neon. See Argon structure.

If each orbit contains maximum 3 electrons, one of them always *stick out* into the **opposite** sides, which is strongly **repelled** by *other* electrons included in the **opposite** ( other ) orbits.

"2 electrons on one side × 4 orbits" can form **stable** regular **tetrahedron**-like distribution from the veiwpoint of each orbit. ( tetrahedron is a part of hexahedron. )

*(Fig.16) Ionization energies show us "where" de Broglie wavelengths change. *

In the same way, **sudden drop** in *inonization* energies show us "**Kr**" and "**Xe**" are the **last** atoms in **4** × and **5** × de Broglie wavelength orbits.

As seen in this and this, the changes of ionization energies from "4s" to "3d" orbitals are **too smooth**, meaning "4s" and "3d" are the **same** type of orbits. Quantum mechanical orbitals are too artificial.

As de Broglie wavelengths (= orbtial radius ) get bigger, the *spaces* between each orbits get **wider**.

So "**packing**" maximum electrons into one *single* orbit ( **5** electrons in **5** wavelength orbit ) causes strong **repulsive** Coulomb forces due to the **imbalance** of electron's distributions in all space.

In Kr and Xe, we consider each orbit contains **3** electrons and makes **6** vertices of regular octahedron ( 3 × 6 = 18 ).

If each orbit contains maxium electrons ( ex, 4 electrons in 4 de Broglie wavelengths ), **half** of them tend to **crash** into *other* orbital electrons on the **opposite** side. See this page

*(Fig.17) *

As I said in this section, as **de Broglie** wavelengths increases, the **midpoint** lines (= zero phase ) increases in number, meaning they can contain **more** orbits *stably*.

In **6** × de Broglie wavelength orbit of Rn, the total **8** orbits can be included due to **increased** *midpoints*. So 4 electrons ( in each orbit ) × 8 orbits become **32** electrons in Rn atom.

Different from 4 or 5 × de Broglie wavelength, the electron's distribution in orbits of 6 × wavelength tend to spread **symmetrically**, when its included number is "3" and "4".

So when the number of electrons is small, this symmetrical distributions in each orbit **obstruct** *other* orbit from being on the **opposite** side.

It is thought that atomic stability is a little more **complicated** in "Hg" (= 26 outer electrons ).

*(Fig.18) Maximum orbits = midpoint lines + 2 (= two perpendicular orbits )*

When each orbit crosses another orbit **perpendicularly**, they can **avoid** destructive interference.

When atoms contain more than two orbits, other orbits must be on the **midpoint** lines (= zero phase ) **NOT** to be disturbed.

So, the maxium number of orbits in Ne becomes "**4**" (= 2 × *perpendicular* + 2 × **midlines** ).

4 × de Broglie wavelength contains **4** midlines, so the total orbital number of Kr becomes "**6**".

The **odd** numbers of "3", "5", "7" orbits are asymmetrical and **unstable**.

So the orbital numbers of "**Ar**" (= 3 × waveslength ), "*Xe*" (= 5 × waveslength ) remain the **same** as "**Ne**" and "*Kr*".

So we can get the generalized **common** rules, "*perpendicular* orbits" and "**avoiding** destructive interference" in all atoms based on **de Broglie** wavelength.

2015/3/25 updated. Feel free to link to this site.