Have you ever tried to hit a moving object? This usually happens in physical education classes when you are supposed to hit your classmates with a ball during a game. Not that easy at all, your opponent is often not that far away from you and can be seen quite clearly.

However, the smaller the goal becomes, the more difficult your task becomes. Now imagine that on a tiny scale! Then you quickly come to the challenge that still occupies scientists today and will probably continue to do so in the years to come. Of course, this involves describing electrons and their location around the atomic nucleus, which is easy to analyze.

## Basics of the orbital model

The idea of orbitals is not new and did not first appear with the orbital model. In fact, this basis has existed since the first detailed atomic model by Niels Bohr in 1913. He developed a system in which the atomic nucleus was at the center and the electrons revolved in orbits around it. You will certainly have already met this model at school. The following figure also shows you the structure of this model.

In the middle you see the nucleus, while the electrons are on the circular orbits around it. These circular paths were later referred to as orbitals. However, they don’t have much to do with reality. The main problem is that this model primarily offers a two-dimensional view. However, this is simply not sufficient to simulate the actual three-dimensional structure of the atoms. The orbital model can help. And that brings you to the actual topic.

## From Bohr to the orbital model

But first things first. Think back to the beginning and remember how hard it is to hit a moving object. It is at least as difficult to describe this object in its movement and its current location at the same time. But that was exactly the goal for the electrons.

Physics provides good help for this, which has also been applied to the electrons. However, none of them were sufficient. In general, due to the size of the electrons, the description was made using light. The location description is quite possible with short wavelengths. At the same time, this also means that this light is particularly rich in energy.

You can now imagine this light as the ball with which you throw your opponent. If you throw your opponent with enough energy, you have definitely determined his position. Most of the time, the ball falls to the ground at exactly this point or bounces off in such a way that you can still determine afterwards where your teammate was.

At the same time, however, you will change his movement yourself, for example by throwing him off balance. At that moment, he no longer moves evenly through the sports hall. Also, the electron will not move evenly like before after you throw it with a ball of light.

Incidentally, the movement that is meant here designates the so-called **pulse** p. This is the product of velocity and mass combined with direction. You experience the effects of such an impulse when you collide with your opponent. If his impulse is big enough, you will be pushed to the side, for example.

Exactly this change in momentum, which took place through a change in movement, was not the goal.

In contrast, you can use a large wavelength for the electrons to be able to determine the momentum in this range. Larger wavelengths have significantly less energy and do not deflect the electrons when they hit them. However, due to their size, they are imprecise when it comes to localization.

The entire problem is summarized under the point of **Heisenberg’s Uncertainty Principle**.

the **Heisenberg uncertainty principle** states that the position and momentum of an electron cannot be determined simultaneously. They can each be determined by individual measurements and then each result in an exact number, but never exactly at the same time.

A solution to this problem came via the **Wave-particle duality** up to **Schrödinger equation**. With that, electrons were no longer simply described as particles. They were also ascribed wave properties. Whole wave functions could be given as a solution for the Schrödinger equations. These were then used to build the orbitals.

Even if the Schrödinger equation is mentioned here only in passing, you should not leave this explanation without knowing what it looks like: HΨ=EΨH\Psi=E\Psi

H stands for the so-called Hamilton operator. This is not considered in more detail here, as it goes far beyond the actual topic. E, on the other hand, stands for the concrete energy that you can express with a numerical value. Ψ (Psi) acts on both sides of the equation, meaning the wave function.

## Structure of the orbital model simply explained

The term orbital in its current meaning was first introduced in 1931 by Robert Mulliken. This artificial word is derived from the English word *orbit*, which means something like «planetary orbit, area». This makes it clear to you why the orbits of Bohr’s atomic model have already been called orbitals. In a way, they resemble the orbits in which the planets revolve around the sun. However, an orbital is now defined as follows:

A **orbital** refers to the space around at least one atomic nucleus in which the electrons are located with a probability of 90%.

An orbital could be described for each electron with the help of the solutions from the Schrödinger equation. This resulted in certain shapes that are characteristic of the respective electrons and their energy.

## The quantum numbers as the basis of the orbital model

The basis of the orbital model is the designation of the individual electrons with so-called quantum numbers. A lot of theory is needed to describe this. In principle, there are four different ones, each of which relates to the properties of this electron. This includes:

- principal quantum number
- secondary quantum number
- magnetic quantum number
- spin quantum number

Quantum numbers themselves come from quantum mechanics, i.e. physics. There they are used to describe states. Applied to our problem of electrons, these quantum numbers serve as state descriptions for the Schrödinger equation.

### The principal quantum number n

The first number given is the principal quantum number. In most cases this corresponds to the period. However, there are also exceptions that you can see in the periodic table. You will learn more about this later, however. The main quantum number is assigned a number from 1 to currently a maximum of 7. The number corresponds to the bowls K, L, M and so on, which you probably also know from the bowl model. Start with 1 at the lowest energy level.

You see the effect of this number mainly in the size of the respective orbitals. An orbital with the principal quantum number 7 is significantly larger than that with a 1.

However, the larger the orbital, i.e. the higher the principal quantum number, the lower the binding energy. In other words, the electrons are always further away from the nucleus and can be removed much more easily.

### The secondary quantum number l

The shapes of the orbitals, which you have already got to know before, are determined by the secondary quantum number. So far there are six possible secondary quantum numbers, i.e. always the main quantum number n-1. The so-called orbital angular momentum is described here. Think back to gym class. The impulse here follows the same principle, just on corresponding tracks.

A little information for you if you can’t remember how many orbitals there are per energy level: The secondary quantum number will help you here too. There are 2l+1 orbitals per energy level. So if you have a secondary quantum number of 1, then there are three orbitals.

The following table shows you the respective secondary quantum number with its assignment to the letters that represent it. In this case, no numbers are assigned. The naming occurs at the beginning on the basis of the spectral shape. However, this has now become irrelevant.

Secondary quantum number orbital meaning l=0s orbitals =* sharp*: sphericall=1p orbitalp = *principal*: dumbbell l=2d orbitald = *diffuse*: two crossed dumbbells l=3f-orbitalf = *fundamental*: rosette-shapedl=4g-orbital alphabetical order: rosette-shapedl=5h-orbital-alphabetical order: rosette-shaped

### The magnetic quantum number m

That brings you to property number three. This results from a fact that you just got to know. The regulation 2l+1 plays an important role again, because it also tells you how many possibilities there are for the magnetic quantum number. The designation is from -l to +l. The 0 in the middle is also included. So the following applies:

m = -1, -1-1,…, -1, 0, +1,…, +1-1, +1

Incidentally, s orbitals always have only one magnetic quantum number, namely 0.

Specifically, the orbital angular momentum is brought into a three-dimensional plane. The z-coordinate in the three-dimensional coordinate system is therefore given via a complex angle calculation. Put simply, this describes the shift up and down.

### The spin quantum number s

It is theoretically possible for two electrons to have the same properties as mentioned above. The distinction is then made via the spin quantum number. This describes the respective angular momentum of the electron. It is specified with a value of +12 or -12.

But all this is difficult to remember and certainly difficult to assign if you have no idea where your element is actually located. But there is great support for that.

## The orbital model in the periodic table

In fact, you can thank the periodic table for this as well. This shows you very simply which orbitals the respective electrons occupy.

So sometimes it can be quite difficult to see through the order. The Mandelung scheme can help you.

Using this scheme, you can easily see which orbitals follow in order, even if you don’t remember their orientation on the periodic table.

Accordingly, an energy level scheme can be created with the information from the periodic table and the Mandelung scheme. As soon as a new orbital is started, you can write it a bit higher. This means that the orbital has a higher energy.

## The box notation in the orbital model

Like any other model, the orbital model has its distinctive notation. While the core is also shown in many other models, it does not play a role here. The focus is particularly on the distribution of the electrons to the different orbitals.

Now that you have an element in front of you, start at the lowest level by filling in boxes representing your orbitals….