2. Atoms: period(Electron shell and s,p,d,f orbitals)

1. Horizontal rows: Periods

The horizontal rows in the periodic table, known as periods, are related to electron shells. Each of these electron shells has a specific energy level. The closer an electron shell is to the central atomic nucleus, the lower its energy level, making it more stable and less reactive. Electrons in the inner shell are strongly attracted to the atomic nucleus and do not participate in activities such as bonding with other atoms. On the other hand, electrons in the outermost shell, which have higher energy levels and higher reactivity glance around at other atoms in the outside world, attempting to exchange electrons. Shells farther from the nucleus have larger radii and greater space, so their energy is higher. So wouldn’t it be possible to deviate from the atomic nucleus? (Those energetic days when I used to sit in the back row of the classroom, trying to break free from the teacher's control and engage in other activities...)

The maximum number of electrons accommodated in a shell

Now, let’s take a brief but thorough look at how electrons exist using the concept of period. We know that the number of an atom represents the number of electrons and there is a rule for locating electrons in the electron shell. Each shell can hold a certain number of electrons. Electrons fill in order, starting from the shell closest to the nucleus. The first shell, or first energy level, contains up to 2 electrons, the second shell contains up to 8 electrons, and the third contains up to 18 electrons. (If the number of shells is n, the maximum number of electrons is 2n² ). We will talk about the reason for this in later part in the orbital. Starting from the first shell closest to the nucleus, they are also called K, M, L, N, etc. shells.

Electron shells and energy level

By understanding how the shells are filled with electrons according to their energy levels, we can get a clear picture. But what happens within each shell? We mentioned that electrons exist within the shells, but can we determine their exact positions? The answer is no. However, we can estimate and calculate the probability of where electrons are likely to be located using mathematical functions. We represent the probability of electron presence as points on a graph and analyze their density. If, for example, I tend to only move between school, home, and the supermarket, and if I mark my location over the course of a year as dots on a map and show the probability of where I might be, the dots would probably be particularly concentrated in those three places, and the space connecting those three places will show you where I am most likely to be. 

Uncertainty principle and Quantum mechanics

The uncertainty principle was formulated by German physicist Werner Heisenberg in 1927. It states that there is a limit to measure precisely both the position and momentum of electrons at the same time at the microscopic scale, such as atoms and subatomic particles. That is, in other words, the more accurately we know the position of a particle, the less accurately we can know its momentum, and vice versa. Particles such as electrons, which have a very small mass and move rapidly, not only have the properties of the particle itself but also have the properties of a wave. Because of this wave-particle duality of particles, the electron's exact orbit cannot be determined until observed, since it exists as a wave before we observe it, but the moment we observe it, it becomes a particle.  This concept is precisely the essence of quantum mechanics. Quantum mechanics is a physics that does not clearly indicate existence but rather indicates existence probabilistically. At this point, our familiar common sense lost its way. I have been fascinated by quantum mechanics and studied it a lot, but I wonder why it seems the more I dig into it, the farther it drifts away.😅

Orbital; subshell

Going back to the concept of an electron shell, the physical region or space where electrons can exist within the shell is calculated and expressed as a probability distribution and then expressed as a 3D shape in 3D coordinates space. We call this "orbital". An orbital is also referred to as a wave function. In other words, orbitals are the concept of subshells within an electron shell, and they can predict the position of an electron up to about 90% accuracy. It is important to note that orbitals are different from the orbits of planets around the sun. It should not be confused. 

It is easy to guess that as the number of shells increases, the radius increases, so the types of orbitals that can exist within them also become more diverse. The farther away from the nucleus, the greater the energy, and electrons fill up the orbitals in order of increasing energy starting from the smallest. Each shell has one or more orbitals(subshells), and the types of orbitals include s, p, d, and f. Electrons are filled into these orbitals in a specific order. By analogy, some texts compare atoms to hotels, electron shells to floors, and orbitals to rooms. This analogy can be a helpful way to understand the concept although it is not perfect in that, for example, p orbital has 3 individual orbitals(rooms). In each room (orbital), a maximum of two electrons can occupy, and they must have opposite spins (Pauli's exclusion principle). If only one electron occupies a room, it will have an "up" spin. (Refer to the electron configuration within the orbital for each period below). Let’s take a brief look at each orbital.

s orbital

In a s orbital, if the probability of an electron's existence is expressed as a dot, it forms a cloud-like sphere centered around the atomic nucleus. In other words, it is probabilistically shaped like a sphere, and two electrons exist somewhere inside it. There is one space (room in the hotel analogy) in the s orbital that can accommodate two electrons inside it. This means that in the first electron shell, which is the closest to the atomic nucleus, there can only be a maximum of two electrons. This corresponds to the completion of the first floor (K shell) in the hotel analogy. A s orbital is present in all and each electron shell and is the first orbital in that electron shell. As we can guess, there will be differences in the radii of the s orbitals of the K shell and that of the L shell. Hydrogen with atomic number 1 and helium with atomic number 2 have only s orbitals in the K shell. 

p orbital

The p orbital has three orbitals in three directions: x, y, and z axes. You can have three spaces (rooms) in each direction, px, py, and pz, and fill them with up to two electrons in that order. That is, a total of up to 6 electrons can be arranged. Therefore, a maximum of eight electrons can be placed in the second electron (L) shell since there are s orbital and p orbitals. In the hotel analogy, it is present in all shells starting from the second floor (L electron shell). Starting from the second electron shell, the p orbital exists in all shells. In the case of Boron with atomic number 5, 2 electrons are located in the s orbital in the first(K) shell, 2 electrons in the s orbital in the second(L) shell, and the remaining 1 electron is placed in the p orbital(px). 

d orbital

There are 5 complexly shaped spaces (rooms) in the d orbital. Each orbital can accommodate a maximum of two electrons, allowing a total of ten electrons to be filled. In the third(M) electron shell, along with the s and p orbitals, the d orbitals are present. Therefore, a maximum of 18 electrons can be accommodated in the third shell. From the third(M) electron shell, d orbitals exist. Argon(Ar), with an atomic number of 18, has all the electrons up to its 3rd electron(M) shell, and these electrons fill the s, p, and d orbitals. 

f orbital 

There are 7 spaces in the f orbital and it can accommodate a maximum of 14 electrons. In the case of the fourth(N) electron shell, it can have a maximum of 32 electrons including across these 4 orbitals. The f orbital exists starting from the N shell. 

In this way, electrons are arranged according to the number of atomic numbers in order from the inside. When completing the f orbital, it starts from the s orbital again.  The diagram below represents the probabilistic distribution of electrons in the s, p, d, and f orbitals in a 3D manner. The x, y, and z axes intersect at the point representing the center of the atom, that is, the atomic nucleus. The colored area indicates the probability of finding electrons within the depicted space.

1s orbital (red), 2p orbital (yellow), 3d orbital (blue), 4f orbital (green)

The Electron configuration notation

Let's take a closer look at how atoms bound to each period across the periodic table fill orbitals for each shell.

Let's take a closer look at how atoms within each period of the periodic table fill their orbitals according to the shell. The electron configuration notation provides information about the distribution of electrons in an atom. The number in front of the orbital indicates the number or order of the electron shell, and the exponent above the orbital indicates the number of electrons in that particular orbital.

For example, in the first period, which consists of hydrogen and helium, the 1s orbital is filled. Hydrogen has one electron in its 1s orbital, while Helium has two electrons filling its 1s orbital. Moving to the second period, we have elements from Lithium to Neon. Lithium has two electrons in the 1s orbital and one electron in the 2s orbital. Beryllium has two electrons in the 1s orbital and two electrons in the 2s orbital. Boron has two electrons in the 1s orbital, two electrons in the 2s orbital, and one electron in the 2p orbital. This pattern continues until Neon, which has two electrons in the 1s orbital, two electrons in the 2s orbital, and six electrons in the 2p orbital. In the third period, which includes Sodium to Argon, we see the filling of the 3s and 3p orbitals. Sodium has two electrons in the 1s orbital, two electrons in the 2s orbital, six electrons in the 2p orbital, and one electron in the 3s orbital.

If we look at the table above, we can notice some patterns. The 1st period(K shell) contains only s orbital, 2nd period (L-shell) contains both s and p, and 3rd period contains s, p, and d orbitals. The periodic table was drawn to reflect those patterns.

In the next article, we will look at the groups of the periodic table.