Example of AUFBAU Principle

The aufbau principle (composition) is a principle of atomic physics, which explains the arrangement of electrons in their orbits around the nucleus of the atom.

The various studies about the nature and configuration of the atom, which allow us to understand its characteristics, has been the subject of study by many researchers. Among them, stands out the work of Niels Bohr, a Danish physicist, who perfected the atomic model proposed by Ernest Rutherford.

His model has the following characteristics: the nucleus of the atom occupies the center, while the electron rotates around in circular orbits. To explain why it does not lose energy in the circular orbit, and taking into account the discoveries of wave behavior and the same particle time that electrons have, he considered that electrons jump from energy level to another, emitting or absorbing Energy.

He knew that these orbital levels are governed by the equation 2n²In other words, the maximum number of electrons in an orbit is equal to twice the square of the number of the orbit. For the elements known to date, we have 7 known orbits, in which the K orbit has 2 electrons, the L, 8 electrons; M has 18 electrons, N contains 32, O contains 50, P contains 72, and Q contains 98.

It had also been discovered that electrons have four quantum numbers: the principal n, which indicates their distance from the nucleus; the azimuthal quantum number, l, which indicates the orbital in which a magnetic quantum number m is located (s, p, d, f, etc), which determines its trajectory within an orbital, and a spin number, s, which can be positive or negative, with a value of 1/2. That two electrons in the same path, (same numbers n and l) cannot have the same magnetic quantum number or the same spin number at the same time. That is, two electrons in an atom cannot have all four equal quantum numbers (Pauli exclusion principle)

This led to the conclusion that for different electrons to coexist at the same orbital level, the levels energetics are divided into sublevels, each of which in turn is divided into orbitals that can only contain a pair of electrons.

According to this observation, the energy level K only contains one sublevel, called the s level, which can be occupied by one or two electrons.

The next level, L, will have four electronic sublevels: a level s, called 2s, and a level called 2p, which in turn is made up of three orbitals, called 2p_x, 2 P_Y and 2p_z. The third level will have the following sublevels: 3s, 3p and 3d. The 3d sublevel will have 5 orbitals, each of which will be occupied by two electrons. The following levels can have orbitals that will be added, with the letters f, g, h and i.

To this we add that when the electrons are not enough to complete an energy level, they are distributed in the orbitals. (Hund's rule).

These sublevels and orbitals are not randomly filled. The electrons in the orbits are organized by filling the lower energy levels first and then the higher energy levels. This is represented graphically, and for that reason it is called the rule of the saw or of the diagonals.

According to the previous rules, the orbital levels of the first 10 elements of the periodic table, represented in the following way:

H: 1s¹
He: 1s²
Li: 1s² , 2s¹
Be: 1s² , 2s²
B: 1s² , 2s²,2 P¹ (1s² , 2s²,[2 P_x¹)
C: 1s² , 2s²,2 P² (1s² , 2s²,[2 P_x¹,2 P_Y¹])
N: 1s² , 2s²,2 P³ (1s² , 2s²,[2 P_x¹,2 P_Y¹,2 P_z¹])
O: 1s² , 2s²,2 P⁴ (1s² , 2s²,[2 P_x²,2 P_Y¹,2 P_z¹])
F: 1s² , 2s²,2 P⁵ (1s² , 2s²,[2 P_x²,2 P_Y²,2 P_z¹])
Ne: 1s² , 2s²,2 P⁶ (1s² , 2s²,[2 P_x²,2 P_Y²,2 P_z²])

As we see in these examples, first the levels with less energy are filled, which in this case are the s levels, and then the p level.

We can also observe that the saturation of the levels occurs with the inert gases Helium and Neon.

In many periodic tables we find as part of the data the electronic structure of the energy levels, and For short, we find in parentheses the inert element prior to the element, and then the rest of the levels orbitals.

For example, in the case of sodium, we can see it represented in either of these two ways:

Na: 1s² , 2s²,2 P⁶, 3s¹
Na: [Ne], 3s¹

Now, if we look at the graph of the sublevels, we will see, for example, that in elements, such as Potassium or Calcium, despite being at level 4, will not occupy the 3d sublevel, since it has higher energy than level 4s. So according to Bohr's rule, level 4s will be occupied first, before 3d:

K: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s¹ - [Ar], 4s¹
Ca: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s² - [Ar], 4s²
Sc: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s¹, 3d¹ - [Ar], 4s¹, 3d¹
Ti: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d² - [Ar], 4s², 3d²

The sequence of the order of the orbitals according to the Aufbau principle and that we can deduce by observing the diagonals of the graph, would be the following:

1s², 2s²,2 P⁶, 3s², 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d¹⁰,5 p⁶, 6s², 4f¹⁴,5 d¹⁰, 6p⁶, 7s²

Examples of the Aufbau principle

Representation of the electronic levels of some elements according to the Aufbau principle:

Yes: 1s² , 2s²,2 P⁶, 3s², 3p² - [Ne], 3s², 3p²
P: 1s² , 2s²,2 P⁶, 3s², 3p⁴ - [Ne], 3s², 3p⁴
Ar: P: 1s² , 2s²,2 P⁶, 3s², 3p⁶ - [Ne], 3s², 3p⁶
V: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d³ - [Ar], 4s², 3d³
Faith: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d⁶ - [Ar], 4s², 3d⁶
Zn: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d¹⁰ - [Ar], 4s², 3d¹⁰
Ga: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d¹⁰, 4p¹ - [Ar], 4s², 3d¹⁰, 4p¹
Ge: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d¹⁰, 4p² - [Ar], 4s², 3d¹⁰, 4p²
Br: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d¹⁰, 4p⁵ - [Ar], 4s², 3d¹⁰, 4p⁵
Kr: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d¹⁰, 4p⁶ - [Ar], 4s², 3d¹⁰, 4p⁶
Rb: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s¹ - [Kr], 5s¹
Sr: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s² - [Kr], 5s²
Y: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d¹ - [Kr], 5s², 4d¹
Zr: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d² - [Kr], 5s², 4d²
Ag: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d⁹ - [Kr], 5s², 4d⁹
Cd: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d¹⁰ - [Kr], 5s², 4d¹⁰
I: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d⁹,5 p⁵ - [Kr], 5s², 4d⁹,5 p⁵
Xe: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d¹⁰,5 p⁶ - [Kr], 5s², 4d¹⁰,5 p⁶
Cs: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d⁹,5 p⁶, 6s¹ - [Xe], 6s¹
Ba: 1s² , 2s²,2 P⁶, 3s² , 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d¹⁰,5 p⁶, 6s² - [Xe], 6s²