The study of physics or chemistry has been one of the fields of research with the most emphasis in all centuries of history. Since the time of the Greeks where the Pythagorean Theorem began to be developed, or even earlier with Thales of Miletus, the first theories were already formed. It was a historical period where the transition from myth to reasoning began to fluctuate. In the early years of history, it was believed that things happened just because or because there was an omnipotent god who acted based on people’s behavior. For example, if it rained or made some kind of storm, many thought it was because the gods had gotten angry and punished them in the form of a storm.
With the passage of time this idea was lost and the reason for things began to be sought. As for example, with theories like those of scientists like Albert Einstein or Isaac Newton. In this sense, today we want to focus on the rule or theory of diagonals, which is used to build and understand the atom or ion from a quantum number point of view, when we observe it from a microscope.
What is the rule of diagonals?
From a general point of view, and before going into detail, the diagonal rule refers to a theory that allows the description of the construction of an atom or ion, but always taking into account the energy level that we can find in each one of the orbits that can be calculated. Therefore, in each of the atoms distribute the energy is regulated by the quantum number that can be calculated. The number that we find in each of the atoms is not something empty, but rather has a certain meaning that helps to know the number of electrons that we will find in each atom. In addition, it is not limited only to that, but also makes a description that allows a better understanding of the properties and characteristics that said atom will have based on the atomic systems that can be deciphered from the position of the electrons and the other parts that make up to the ion or atom.
Likewise, the rule of diagonals, or Madelung’s rule depending on the context in which we find ourselves, is also aimed at making an exhaustive description of the behavior of each of the electrons within chemical components. The use of this rule is variable, and part of another principle that is based on Aufbau’s theory. Founded by the scientist Niels Bohr, who decided to adopt the name Aufbauprinzip, which means construction principle in German, it comes to tell us that protons tend to align one by one in the nucleus of the atom, while electrons play exactly the same role. in the orbit of the atom forming a gradual and proportional process within the atom itself. This principle also allows us to decipher two things using the commutative property of mathematics, the one that says the order of the factors does not alter the product. If an atom is in its normal and usual state, this will mean that the electrons will align in atomic orbitals. But, it can also be seen from the opposite direction. If the electrons align correctly, this means that the atom will be normal and therefore the protons will align proportionally with respect to the nucleus. It is necessary to know it as well as the difference between an ionic bond and a covalent bond.
In addition, another of the properties of the electrons within the atoms is that they are located in order from lowest to highest, that is, first the electrons with the lowest energy and later and successively those with the highest energy. The diagonal rule also provides a better understanding of all electronic elements that are found within the atom itself, with special emphasis on when the ion is in its fundamental state. This is one of the main keys to this theory, since if the atom changes state for any reason, this rule will no longer be valid for what we are looking for, which is to know the electronic state of each of the atoms in their current state. base. The importance of this electronic understanding is essential, since when it is possible to understand these aspects, much more information is also obtained about the properties of each of the chemical elements present in an atom.
In fact, the importance of the diagonal rule was such that it helped to structure the elements of the periodic table in this way and not in another. The investigation of the chemical elements was what allowed, to a large extent, that today many high school students can have a periodic table that they must study to understand the structure of the different chemical elements such as sodium or phosphorus, among others. The normal thing is to study the atoms from their natural point of view but it is also possible to do it in the elements of the periodic table. According to the exclusion principle that Pauli formulated, the rule of diagonals makes it clear that when two electrons are part of the same atom, it is impossible for said particle to have two absolutely similar quantum numbers. An atom will be made up of four quantum numbers, and each of them will be in charge of describing the state of the different electrons present in the atom itself.
Benefits of the diagonal rule
All in all, the rule of diagonals has meant an enormous advance for science and the atomic study of the different elements of the periodic table that has allowed progress in the emergence of new techniques both in the field of physics and chemistry. The most prominent are:
- Preparation of the periodic table. The rule of the diagonals, as we have commented previously, has contributed to the elaboration of a periodic table in which all the chemical elements can be observed with their composition in electrons, neutrons and protons in a scaled and ordered way.
- Educational advancement in schools. This periodic table is a mandatory content in schools and a student who obtains the basic school graduate without having passed natural sciences and, therefore, has studied and learned the elements of the periodic table, obviously without being a specialist, is inconceivable.
- Emergence of new investigative techniques. The rule of diagonals supported new elements in the understanding of something as simple, but at the same time as complex as an atom. Therefore, this theory has allowed new lines of research to be opened that have contributed to science.
- Understanding of the atom. The atom is something basic since it is the smallest particle that can be found in any type of element. However, it is also difficult to understand and therefore many people can develop a professional career related to their research.
The rule of diagonals, as it happens with multiple scientific theories, would be nothing if it is not put in parallel with other types of theories. Something that is related to this is Hund’s rule, which in a few words, predicted that in the sublevels of the atom the one that presented a greater number of spins in its orbitals is also the one that was more stable. It is a bit similar to what happens with the rule of diagonals and the structure of electrons and quantum numbers that we will see next.
How the rule of diagonals is applied:
Before learning about the application of the diagonal rule, it is worth taking a deeper look at the quantum number, and the different options it offers. For one thing, don’t forget that there is no single version of this number. The main one focuses on the number of electrons that make up the atom itself, while the azimuthal analyzes the ion itself from a more geometric point of view, giving data about the angle and the way in which the orbital is composed. These two concepts are essential to understand this theory. Finally, we can also find two more types of quantum numbers that are worth mentioning. The magnetic type quantum number is more oriented to the orientation that it may have in space, while finally the spin quantum number refers to the direction that the path of the electron may have on its own figure.
In accordance with the rule of diagonals, Hund warned that if we observe the sublevels of atoms, we can also use the commutative property of mathematics, the one in which the order of the factors does not alter the product. What this scientist of German origin was saying is that the atom itself will be more stable depending on the number of spins it has in parallel in each orbital. In this sense, an atom that has many spins will have a really high stability, while that atom in turn, if it is stable, will also mean that it has a large number of spins. Therefore, following Hund’s approach, the rule of diagonals allows a fully proportional distribution of the number of electrons ordered from lowest to highest energy level to achieve said stability as a function of the quantum number of each particle. Therefore, to better understand the atom, an exhaustive study of the periodic table is necessary to understand each quantum number and the distribution of its electrons.
Obviously, as in all theories, we must also look carefully at all the exceptions that we can find, which can be many. As we have said before, the rule of diagonals is only valid as long as the atom is in its fundamental state, that is, its electronic charge is zero and it can be related to any element on the periodic table. In any other case, it cannot be applied except for the exceptions that we will discuss below. Some materials such as palladium, chromium and copper have some kind of deviation that causes their ground state to occur when their electronic configurations are partially filled. In this sense, these would be in general lines the three exceptions that can be found since its fundamental state is inversely proportional to the amount of energy from electrons that it receives. Undoubtedly, the rule of diagonals was a great advance in the manifestation and formation of the periodic table and opened up new lines of research to better understand the structure of atoms and all the elements that surround it. A new challenge for science and all the people who spend the day locked in a laboratory looking for new challenges like the discovery of cellular respiration.