How exactly electrons operate outside the nucleus of an atom is actually confusing to many people.

There are still many people today who mistakenly believe that electrons move around atoms in the same type of motion as the Earth moves around the Sun, and that's just plain wrong!

You may know about Ball's energy leap model, the electron cloud model, but you still don't know much about how electrons actually move.

Then let's start with the analysis of the energy leap of Bohr. An electron jumps from one orbital to another, the process of jumping is discontinuous and there is no transition.

# Misconceptions about atomic orbitals

Here it is important to clarify the concept that many people will mistakenly think that atomic orbitals are the electron layer orbitals outside the electron nucleus.

In fact, these 1, 2, 3 "orbitals" are not atomic orbitals, they are energy layers, also called electron layers.

The energy layers are the K, L, M, N, O, and P electron layers of high school chemistry, and the corresponding electron layer numbers are 1 2 3 4 5 6 in that order.

The first layer is also called the K layer, the second layer is the L layer, and the third layer is the M layer (and so on). Each electronic layer (energy layer) in turn contains different energy levels, and the number of energy levels in an electronic layer depends on the serial number of the electronic layer.

For example, the first electron layer (K) has only one energy level. The second electronic layer (L) has two energy levels (and so on). Because energy levels are subordinate to electronic layers (energy levels), they are also called electronic sublevels. Energy levels are actually the s, p, d, and f atomic orbitals learned in high school chemistry.

For example, the first electron layer has only one energy level, and this energy level is the s-orbital. The second electron layer has only two energy levels, which are the s- and p-orbitals, respectively. The third electronic layer has three energy levels, these three energy levels are s, p, d orbitals. The rest of the electron layer, and so on.

But be sure to note that the second electron layer has two energy levels, not that there are only two atomic orbitals, s and p.

All tracks except the s-track come with a copy function (strictly spatial orientation). s-track is spherical, this kind of track does not copy itself, so it exists alone. p-track has a dumbbell shape, this kind of track comes with a triple copy function, d-track are all three d-tracks appearing together. d-track comes with a quintuple copy function, d-track are all five appearing together.

The copy multiplier of the spdf track is calculated in the odd form of 1, 3, 5, 7, etc. In fact, the so-called spdf orbitals just indicate the different shapes of the electron cloud. Electron probability will appear in a particular space, it so happens that such a space will form a particular shape. For example, s orbitals are like spheres, p orbitals are like dumbbells, and d orbitals are like flower petals.

Now that we have figured out the types of atomic orbitals, the next step is to see how exactly electrons occupy these orbitals.

In fact, the process of electron occupation of atomic orbitals proceeds mainly according to the bubbly incompatibility principle and Hundt's rule.

The Pauli incompatibility principle tells us that an atomic orbital holds at most two electrons.

For example, the first electron layer (K layer) has only one energy level, and there is only one s orbital on this energy level, so it can only hold two electrons.

The second electron layer (L layer), has two energy levels, s and p, so there is one s orbital and three p orbitals, for a total of four atomic orbitals, so it holds up to eight electrons.

The third electron layer (M layer), has three energy levels s, p, and d, so there is one s orbital, three p orbitals, and five d orbitals, for a total of nine atomic orbitals, so it holds up to 18 electrons.

In nature, everything strives for stability, and if it is not stable now, it will always reach a stable state.

Because stable things change less, unstable things change a lot, and a state that changes a lot always tosses to a state that changes less.

The same applies to physics. A stable state means low energy, and the most stable state, the energy is in the lowest state.

And Hundt's rule is simply the lowest energy principle, where electrons always occupy the lowest energy atomic orbitals first, and are only forced to occupy higher energy atomic orbitals if the lower energy ones are filled. After understanding Hundt's rule, all that remains is to compare the energies of different atomic orbitals.

The energy of these atomic orbitals is such that

1s is the s orbital of the first electron layer, 2s is the s orbital of the second electron layer. 2p is the p orbital of the second electron layer (the first electron layer has no p orbital)

According to the horizontal comparison, 1s is less than 2s is less than 3s. 2p is less than 3p is less than 4p.

According to the vertical comparison, 3s is less than 3p is less than 3d.

According to the horizontal and vertical contrast, the principle of energy staggering is involved. From the fourth electron layer, 4s is less than 3d. After the energy staggering comparison, check the information on your own, I will not expand on it.

# Deeper understanding of the bubbly incompatibility principle

I wonder if you've ever wondered why the Bubbleley's disphase principle holds that an atomic orbital can only hold two electrons? First imagine that there are many electrons distributed outside the nucleus of an atom, are they all the same?

If you just intuitively feel as if all the electrons look the same. In the conventional way we cannot identify any difference between two electrons.

But when you think about it rationally, you think there must be a difference between the electrons.

In fact, there are indeed many differences between electrons

To distinguish the electrons. So it is necessary to develop a special way to give these electrons an identification number.

In quantum mechanics, there are several quantum numbers for the existence of several different points of the electron. So there may be many kinds of quantum numbers.

And for the off-nuclear electrons, generally only four types of distinctions are made, so there are four quantum numbers.

If two electrons have the same four quantum numbers, then they have the same quantum state and it is impossible for them to be in the same atomic orbital. This is the rigorous explanation of the Bubbleley incompatibility principle.

But why is it that the Bubbleley's disphase principle concludes that an atomic orbital holds at most two electrons. How can this be understood?

To explain this, we need to first understand the four quantum numbers of electrons, that is, the four ways of differentiation.

The first distinction is the principal quantum number

For example, the electron in the first electron layer and the electron in the second electron layer are both extra-nuclear electrons, but they are in different electron layers, so the first difference comes out. This is the principal quantum number.

The second difference is the angular quantum number

For example, the second electron layer has four electrons. First of all, these four electrons have the same principal quantum number, but they may have different types of orbitals between them, such as s orbitals or p orbitals, so dividing them according to atomic orbitals gives another way to distinguish electrons.

The third difference is the magnetic quantum number

As I have just said, there are three p-orbitals in the second energy layer, and if all three p-orbitals have electrons, their principal quantum numbers and magnetic quantum numbers are already the same at this time.

It is no longer possible to distinguish the three electrons in the three p-orbitals of the second energy layer if only by the first two ways.

In fact, the three p-orbitals are not identical, because different p-orbitals have different components on the magnetic field. This is the third difference.

Now you imagine if the bubbly incompatibility principle only applies to these three quantum numbers.

Then only one electron can fit in the same atomic orbit at the same energy level.

Because once two electrons exist in the same atomic orbital, then the three quantum numbers of these two electrons must be the same, so it will violate the bubble incompatibility principle.

This time, the fourth distinction is particularly important. Without the fourth distinction, there cannot be two electrons in an atomic orbital, but only one. This is the fourth quantum number, also called the spin quantum number.

There are only two spin quantum numbers, either -1/2 or 1/2. The two spins can be roughly thought of as either up or down spins.

So the first three quantum numbers of both electrons within the same orbital are the same, but the fourth quantum number is different, and only two can be different, either spin up or spin down. So an atomic orbital must hold only two electrons with different spins.

In fact, it is the fact that there are only two differences in the fourth quantum number that leads to the fact that only two electrons can exist in the same orbit, which is the core idea of the Bubbleley incompatibility principle.

In fact, there is a deeper explanation for the fact that four electrons with the same quantum number cannot be in the same orbit.

Since electrons are wave functions by nature and are anti-symmetric.

The antisymmetric wave function means that two electrons with exactly the same quantum number meet and will constrain each other. One of the electron waves goes up, the other one must go down and correspond strictly.

Once the two waves are in the same orbit, then the meeting will be completely canceled, thus causing the wave function of the electron to disappear, and that electron will not exist.

The antisymmetric wave function of electrons also explains essentially the bubble incompatibility principle.

Imagine if there were no bubbly incompatibility principle, then all the electrons outside the nucleus would occupy the lowest energy ground state atomic orbitals according to Hundt's rule. All electrons, if in the ground state, would be chemically as stable as a helium atom.

If basically all atoms in the universe were in a stable state, they would not easily form chemical bonds, then organic matter would not exist, and life would not naturally exist.

So from this perspective, there is one more person to thank for the existence of life on Earth.

Mankind must thank not only gravity, electromagnetic force, dark energy, supernova explosion ejected heavy elements, the Sun's energy, the Earth's magnetic field, Jupiter's guards, underwater hot springs formed luca, but also nature has created the bubbly incompatibility principle!