Atomic Models – Periodic Table

The elements of the periodic table are arranged according to the number of electrons. The Bohr atomic model cannot explain the number of electrons in the respective periods, or shells, very well.

What about our vibrational modes of electrons in the quantum dimension? Can we explain the periodic table by counting nodal lines?

Let us assign the possible vibrational states to the keys of an organ. The organ manuals correspond to the energy levels n=1, 2, 3, and so on. An electron can excite a specific vibrational state. The key is then pressed, so to speak, and the corresponding vibration is activated. Two electrons press two keys – at least! The more electrons are present, the more keys are pressed.

But first things first. The first electron occupies the vibrational state at the lowest energy level, that is, n=1.

In a 1s orbital, spin up and spin down have almost the same energy. The spin can thus point in any direction. Superpositions may happen. The hydrogen atom, which is the simplest atom, having only one electron, is also the most frequently occurring chemical element in the universe.

According to the so-called Pauli Exclusion Principle, a second electron cannot occupy exactly the same state as the first. When there are two electrons in the 1s orbital, they occupy two different spin states – up and down. We have thus filled the first shell. The corresponding element with two electrons is the noble gas helium.

The third electron has no place left in the bottom shell. It must occupy a state with one nodal line in the second shell; again, this is due to the Pauli Exclusion Principle.

Radial nodal lines are more advantageous than azimuthal lines in terms of energy. This is why the 2s orbital is occupied first, and not the 2p orbital. This single electron is very reactive. It is thus, significantly, the highly reactive alkali element – lithium.

The fourth electron occupies the other spin state in the 2s orbital. This corresponds to the element beryllium.

For the first time, an electron occupies a state with an azimuthal nodal line: It is the fifth electron, which corresponds to the rare semimetal boron.

Six electrons correspond to carbon. Negative electrons repel each other, and the p orbital can take more states. That is why, at this step, the electron does not complete the spin, but fills the next p orbital instead. This happens according to the so-called Hund’s Rule.

With nitrogen, all p orbitals are filled once. It is only with oxygen that a p orbital is filled twice.

The next in line is fluorine. Finally, the noble gas neon completes the second shell.

We have thus explained the arrangement and number of elements of the first two periods of the periodic table. S orbitals can accommodate a maximum of two electrons; p orbitals a maximum of six electrons. The far right section of the periodic table lists noble gases. The shells of those elements are filled completely. Here, a lot of energy is required to free an electron from its ground state.

Let us now fill our third shell with electrons, following the same principle. For a better overview, let us pull the organ manuals apart a little. We have, again, two elements with 3s electrons, six elements with 3s and 3p electrons, and another 10 elements with 3s, 3p, and 3d electrons.

Wait a second! You may have noticed that two elements are missing. Where are the elements 19 and 20 – potassium and calcium? How can we explain the break in the arrangement between argon and scandium?

We have seen a similar situation at the 2s orbital. Radial nodal lines are more advantageous than azimuthal lines in terms of energy. Thus, electrons prefer to fill them first.
Even though, in this case, we have one nodal line more, the electrons prefer the 4s orbital with two possible states. This arrangement corresponds to the two missing elements.

But why doesn’t the 21st electron simply continue at the 4p orbital, but switches to the 3d orbital instead? Once more, we are presented with the question: what is more favourable for an electron: one azimuthal and two radial nodal lines, or two azimuthal nodal lines?

In this case, the lower total number of nodal lines proves to be more advantageous. We lift, so to speak, our organ manual, and the 3d states can be filled in logical order.

The 3d orbital consists of 10 so-called sub-group elements. All of them are transition metals, such as iron. Only then the six 4p orbitals follow, up to krypton, which has a total of 36 electrons.

In the 4d orbital, two azimuthal nodal lines and one radial nodal line are available for the 37th electron. However, this electron also follows the previous pattern. The 4 radial nodal lines of the 5s orbital are more favourable for the electron in terms of energy, and it prefers to fill the 5s orbital. The electron starts a new period.

For the 39th electron, again, the lower total number of nodal lines proves to be more advantageous than the number of nodal lines on the 5p orbital. The 4d states are filled with 10 further sub-group elements. All of them are transition metals, such as palladium.

The six 5p orbitals follow up to the noble gas xenon with 54 electrons.

The 55th electron can now fill a 6p orbital with 10 states, and, for the first time, a 4f orbital with 14 states. What decision will it take? Three azimuthal nodal lines, or two radial and two azimuthal nodal lines?

When two people quarrel, a third rejoices. The 6s orbital with 5 radial nodal lines is still more favourable than the two opponents, and is gets filled.

The energy levels of the 5d and 4f orbitals mix, and form the basis for the next 24 elements.

This is followed by six elements. The 6p orbital gets steadily filled.

The 87th electron also occupies the 7s orbital without azimuthal nodal lines. The 6d and 5f orbitals mix again, and form the basis for the elements 89-112.

Finally, the 6 states of the 7p orbital are filled. The elements 113-118 of the periodic table are thus complete. None of these elements has stable isotopes. They all decay radioactively within a short time.

The Bohr atomic model described the shell structure of the atom for the first time. It could not, however, explain the exact structure of the periodic table. With Chladni’s help, we have managed to extend the model, and to rediscover the s, p, d, and f orbitals in the quantum dimension.

But that is not the end of the story. It is just the beginning of the music of a quantum organ.