Every element in the periodic table has different number of electrons organized in shells. Each shell can hold a certain number of electrons and when the outer shell fills the result is an inert element like Neon. Each periodic table row ends in an inert element that doesn’t chemically react because it doesn’t exchange electrons. In contrast, other elements do exchange electrons in chemical reactions. Every chemical reaction, from acidity to oxidation, is atoms exchanging electrons to complete their outer shells in the now familiar search for stability. Atoms form stable molecules when those with extra electrons donate them to those with deficits giving chemical bonds that complete the shells of both parties.

The current electron shell description is based on two quantum numbers:

1. Shell * n* (1, 2, 3 …). Was initially the orbit radius.

2. Sub-shell l (s, p, d …). Has no clear meaning.

The s, p and d sub-shells were deduced from spectroscopic data analysis to contain 2, 6 and 10 electrons. Electrons then fill shells and sub-shells according to quantum numbers. In the initial model, inner orbits with fewer electrons filled before outer orbits and so the periodic table grew. Doubling the first orbit of two electrons quadrupled the orbit area to allow eight electrons, tripling allowed eighteen, quadrupling it thirty-two and so on. Hence the first row of the periodic table has two elements, Hydrogen and Helium and the second row has the eight elements Lithium-Neon.

This worked nicely but the third row is still only eight elements, including the carbon and oxygen we need to live, and the expected eighteen elements only occur in the next row. As Table 4.7 shows, the initial model predicted periodic table rows of 2, 8, 18, 32, 50 and 72 but instead the rows were 2, 8, 8, 18, 18, 32 and 32. So in the by now well-established practice, theory was fitted to fact by tweaking the quantum numbers so the sub-shells occur in this odd order:

Row 1: 1s Hydrogen-Helium (two elements)

Row 2: 2s, 2p Lithium-Neon (eight elements)

Row 3: 3s, 3p Sodium-Argon (eight elements)

Row 4: 4s, 3d, 4p Potassium-Krypton (eighteen elements)

Row 5: 5s, 4d, 5p Rubidium-Xenon (eighteen elements)

Row 6: 6s, 4f, 5d, 6p Cesium-Radon (thirty-two elements)

Row 7: 7s, 5f, 6d, 7p Francium-? (thirty-two elements)

The “logic” here is that it works. The third shell “fills” with one of its sub-shells empty, so generations of chemistry students have had to learn that Argon completes its third shell without the 3d sub-shell, even though that denies what a sub-shell means. If they asked why, the answer was because it does!

Instead of describing electrons by quantum numbers we invent, electrons as quantum waves expects these properties:

1. Shell. A sphere circumference around the atom nucleus that fits the electron as a quantum wave.

2. Sub-shell. A higher wave frequency that the shell circumference allows.

3. Direction. The electron wave direction, where quantum waves at right angles don’t interfere.

If an electron is extreme photons entangled in a collision on one axis, its other axes will also have entangled photons. If these are also extreme photons, they will be up one cycle and down the next so the minimum shell circumference is half this wavelength. This fundamental harmonic is currently called the * s* sub-shell.

The next shell will have a circumference double that of the first shell. This allows not only another fundamental but also a second harmonic that is twice the frequency. This second harmonic is currently called the d sub-shell. Figure 4.23 shows how a given shell circumference can accommodate different harmonics to represent different sub-shells. The number of waves that can concurrently occupy each harmonic is given on the right-hand column.

The periodic table can now be explained in terms of electron waves as follows:

1. The first shell has a half wavelength circumference so a bipolar wave can go up and down on alternate cycles (Figure 4.23a) as the first harmonic of the first shell or 1s sub-shell. This shell can accommodate two waves at right angle directions so the first shell completes with two electrons. This gives the first row of the periodic as Hydrogen plus the inert gas Helium.

2. The second shell has a one wavelength circumference compared to the first and the first harmonic again alternates up and down at this length giving a 2s sub-shell with two electrons. The second harmonic (Figure 4.23b) can accommodate two electron waves at the same time which for two directions is four electrons. The extra harmonics of two-dimensional waves such as appear on a drum surface allow two more electrons, giving six in total for the 2p sub-shell. The second shell total is thus eight electrons, giving the second row of the periodic table Lithium to Neon.

3. The third shell has a one and a half wavelength compared to the first as it triples the first circumference. This again gives 3s and 3p sub-shells but the next harmonic can’t occur. A bipolar (up-down) wave can vibrate once on a string half its wavelength and twice on a string of the same wavelength but it can’t do more on a string one and a half times that as the result self-destructs. Adding another half-wavelength adds no new harmonics so the third shell, like the second, allows only eight electrons giving eight elements in the periodic table third row. A harmonic wave model has no 3d sub-shell.

4. The fourth shell has a two-wavelength circumference compared to the first. Four times the first radius allows a new harmonic that accommodates four electrons per circumference which for two directions is eight (Figure 4.23c), plus two complex harmonics is ten. This 4d sub-shell plus the 4s and 4p sub-shells gives the eighteen elements of the periodic table fourth row.

5. The fifth shell, like the third, allows no new harmonic, so its 5s, 5p and 5d sub-shells repeat the previous total of eighteen, giving the periodic table fifth row.

6. The sixth shell allows a new harmonic with six electrons per axis (Figure 4.23d), which doubled again is twelve, plus two complex harmonics is fourteen. This plus eighteen from the s, p and d harmonics gives the thirty-two elements of the sixth periodic table row and the seventh orbit also has 32 elements.

An electron wave model fills the periodic table as follows:

1s Hydrogen-Helium (2 elements)

2s, 2p Lithium-Neon (8 elements)

3s, 3p Sodium-Argon (8 elements)

4s, 4p, 4d Potassium-Krypton (18 elements)

5s, 5p, 5d Rubidium-Xenon (18 elements)

6s, 6p, 6d, 6f Cesium-Radon (32 elements)

7s, 7p, 7d, 7f Francium-? (32 elements)

Electrons now fill shells and sub-shells in strict order, with no strange jumping between them, based on:

1. Shell. The first shell circumference is half the wavelength of the highest frequency of light, i.e. a Planck length. The following shells are multiples of this (1, 2, 3, 4, …).

2. Sub-shell harmonic. Where* s* is the first harmonic, *p* is the second harmonic, and so on.

3. Direction. The great circle axis orientation, where opposite waves don’t interact.

Electrons fill in the order they do based on:

1. Shell order. Each shell is a greater circumference. If an electron were pure light a longer wavelength would be less energy but it has mass so larger orbits require more processing, i.e. more energy. Shells fill in the order 1, 2, 3 etc. because smaller orbits need less processing.

2. Harmonic order. Each sub-shell harmonic is a shorter wavelength for the same orbit circumference, so it involves more energy. Sub-shells fill in the order s, p, d etc. because lower harmonics need less processing

An electron wave model explains the rows of the periodic table as caused by the harmonics that a shell circumference can accommodate, so electrons fill the shells with no tweaks needed.

In quantum realism, electrons in atoms are quantum waves whose behavior is better described by wave harmonics than abstract quantum numbers.