The atom - Electrons, shells, and orbitals

The electrons' movement around the nucleus is often described as shells and erroneously drawn as concentric circles/shells (fig. 1). Starting with the concentric circles, also known as The planet model, this is a model suggested by Niels Bohr. In the Bohr model the circles or shells are called k, l, m, etc. from the nucleus out. In the k shell you can have 2 electrons and the following shells you can have 8 electrons. As a working model it works fairly well for simplified chemistry, which is most likely the reason it is still in use despite its flaws, but modern chemistry requires the use of a correct model. Therefore: Know that it exists, it is an important part of history, but when working in science, use the correct description.

The correct description of how the electrons move around the nucleus is called orbitals. We have four basic types of orbitaler: s, p, d, and f. Each orbital has its own architecture and properties. For historical reasons we use the name shells and call them k, l, m, etc. as in the Bohr model. They are not shells like in the Bohr model, which can cause some confusion. Here the shells are groups of orbitals.

The shells, i.e. the groups of orbitals, also represents energy levels. The inner electrons/orbitals have the lowest energy level and the strongest binding to the nucleus. The binding energy decreases with increasing distance to the nucleus. The atoms aim for the lowest possible energy level, so the shells are filled with electrons from the k shell out, i.e. first the k shell is filled, then l, m, n, etc. In practice it is not this simple, so e.g. parts of the n shell is filled up before the m shell is completely filled. This is one of the places where our models have some weaknesses when it comes to describing the real world. The how and why this is, is addressed below.

The electrons in the outer shell is also called valence electrons.

Why is this important?

• The presence of orbitals can explain why the periodic table of elements looks the way it does.
• The difference in orbitals can also explain why some bonds between atoms are stronger than others.
• The chemical properties are a direct result of the orbitals. So, many of the things happening in chemistry will make much more sense when we get to them.

Let us take a closer look at the shells and orbitals.

s orbitals are spherical (awaiting figure 2). They are the closest thing we have to the shells in the Bohr model. An s orbital can contain 2 electrons.

The k shell consists of one s orbital, which is why we can only have 2 electrons in the k shell.

p orbitals consists of three identical orbitals. Each of these looks like two droplets connected at the pointy ends, and the three orbital are perpendicular to each other (awaiting figure 3). The architecture means that they each have a positive and a negative end. Each of the three p orbitals can contain 2 electrons, so the p orbital can contain a total of 6 electrons. To tell the three p orbitals apart, they are called p_x, p_y and p_z, referring to their orientation in a coordinate system. This is usually something used for orbital calculations. For common use in practical chemistry, we just work with one p orbital consisting of 3 orbitals and up to 6 electrons.

The l shell consists of one s and one p orbital, which is why we can have 8 electrons in the shell. The gas neon (element no. 10) therefore has 10 electrons moving around, 2 electrons in the k shell (one s orbital) and 8 in the l shell (one s orbital having 2 electrons and one p orbital having 6 electrons).

d orbitals consists of 5 orbitals, each containing 2 electrons. The orbitals' architecture is as shown in fig. 4 (awaiting figure), and though they may look a little strange, this is not what makes d orbitals interesing. We will get back to the d orbitals, when we take a closer look at the periodic table of elements and the formation of ions. d orbitals are important, as they are the reason why the group of elements called transition metals, behave the way the do.

The m shell consists of one s, one p, and one d orbital, which is why there can be 18 electrons in the shell. At the m shell, our normal rule about filling the shells with electrons goes wrong. The d orbitals in the m shell have a higher energy level than the s orbital in the n shell, therefore this happens: the s and p orbitals in the m shell are filled first. This is up to the element argon. After this, the s orbital in the n shell is filled, this is the elements potassium and calcium, and only after this, at scandium, the d orbitals in the m shell are filled.

f orbitals consists of 7 orbitals, where each can contain 2 electrons. The orbitals' architecture is as shown in fig. 5 (awaiting figure). As it can be seen, the orbitals are different from the other types of orbitals. The f orbitals are the ones giving the rare earth metals, lanthanides and actinides, their chemical properties.

Besides the s, p, d and f orbitals, the s and p orbitals, in the outer shell, can also form hybrid orbitals, if the conditions are favorable. The orbitals are called sp, sp₂ and sp₃ orbitals, depending on whether an s orbital is mixed with 1, 2 or 3 p orbitals. The hybrid orbitals can be seen in fig. 6 (awaiting figure):

As seen, the hybrid orbitals' architecture reflect the ratio of in mixture. Like the original orbitals, the hybrids can contain 2 electrons each. Hybrid orbitals especially seen for carbon, silicium and germanium, and they are the reason that the organic chemistry is the way it is.

As some may have noticed by now, electrons occurs either single or in pairs in the orbitalerne. These are referred to as either unpaired or paired electrons. Paired electrons in the outer shell are called a lone pair.

The electron moving around the nucleus is rotating as well, which makes it slightly magnetic. This is referred to as the electron's spin. An electron where the orientation of the spin is irrelevant is written as e⁻, whereas electrons with a spin is written as ↑e⁻, or just ↑, at spin up (spin quantum number m_S = +½), and similarly ↓e⁻, or just ↓, at spin down (spin quantum number m_S = −½). Spin quantum numbers and the Pauli exclusion principle, which is where this belongs, will be addressed in another chapter. Two electrons in an orbital will act like common magnets and paire north pole with south pole. When talking about electrons in pairs, they are said to have opposite spin, which is usually written like this: ↑↓.

Is it possible to have more than 2 electrons in an orbital? No, not possible. According to the Pauli exclusion principle, only one electron is allowed per quantum state, and electrons only have two quantumstates +½ and −½.

Electrons are added to the orbitals from the lowest energy level and up. If you have multiple orbitals with the same energy level, as seen for p, d, and f orbitals, the general rule is that first one electron is added to each orbital. The second electron, for making pairs, is not added until all orbitals having the same energy level contains one electron. The rule about electrons being added to orbitals with the same energy level one at a time, not forming electron pairs until all orbitals contain an electron, is called Hund's rule (after the German physicist Friedrich Hermann Hund). It is important to keep in mind that this is only a general rule. Exceptions are common. The way the electrons are organized in the orbitals is called electron configurationen, and is written as the orbital + number of electrons in superscript, i.e. 2 electrons in the first s orbital will be 1s² and in the second s orbital 2s². The only way for this to make sense is by lookin at some examples. These will be shown in the next section.

Fig. 7: Relative energy levels for orbitals (click to enlarge).

There is, in reality, only a limited number of orbitals. In theory there is an infinite number of orbitals, but scientist have struggled many years just to get to Oganesson, element no. 118, and after element no. 105, the halflife drops to a few seconds or less. De tilgængelige orbitaler og deres relative positioner i forhold til energi, er vist på figur 7.

The simplest way of working with electron configurations is for neutral gaseous atoms at the ground state, i.e. when the atom is not affected by anything. Starting from the bottom with element no. 1, hydrogen, which has one electron, which is placed in the first orbital 1s (fig. 8). The electron configuration is 1s¹. The second element, helium, has 2 electrons. With only one electron in 1s, the electrons must be paired (fig. 9) and the electron configuration becomes 1s².

Fig. 8: Electron configuration for hydrogen (click to enlarge)	Fig. 9: Electron configuration for helium (click to enlarge)

Elements 3 and 4 fill up the 2s orbital, and element no. 5, boron, starts using the 2p orbital (fig. 10). The electron configuration for boron is 1s²2s²2p¹. The next element, carbon, does not have 3 pairs of electron at the surface, but starts filling the other orbitals with single electrons (fig. 11) and at element no. 8, oxygen, the pairing begins (fig. 12).

Fig. 10: Electron configuration for boron (click to enlarge)	Fig. 11: Electron configuration for carbon (click to enlarge)	Fig. 12: Electron configuration for oxygen (click to enlarge)

As it can be seen, the electron configuration becomes a rather long line of letters and number, potassium would be written as 1s²2s²2p⁶3s²3p¹, so a truncated version is made from the noble gas that came before, written in square brackets, + electrons added after this. For potassium it looks like this:[Ar]3p¹.

For the first three periods the spatial arrangement and the energy levels follows each other, until we get to the d orbitals. As seen in fig. 6, 4s has a lower energy than 3d. So, what happens is that 4s is filled, which gives calcium the electron configuration [Ar]4s² (fig. 13), and the following element, scandium, will then start filling out the 3d orbitals, and thus have the electron configuration [Ar]3d¹4s² (fig. 14). Notice that eventhough 3d is filled out after 4s, it is written before 4s i.e. the hierarchical structure in the numbering takes precedence over the actual order in which the electrons are added.

Fig. 13: Electron configuration for calcium (click to enlarge)	Fig. 14: Electron configuration for scandium (click to enlarge)

As mentioned earlier, exception to how the orbitals are filled with electrons can be found. Iridium has the electron configuration you would expect: [Xe]4f¹⁴5d⁷6s² (fig. 15). Platinum, following this, should have been [Xe]4f¹⁴5d⁸6s² i.e. another electron in the 5d orbital, but it is not. Instead the electrons are rearranged, moving a 6s electron to the 5d orbital, so the actual electron configuration becomes [Xe]4f¹⁴5d⁹6s¹ (fig. 16).

Fig. 15: Electron configuration for iridium (click to enlarge)	Fig. 16: Electron configuration for platinum (click to enlarge)

The only elements having a stable electron configuration at ground state are the noble gasses. All other elements will try to arrange the outer shells, or at least the outer orbitals, to obtain the same stability. This is done by either taking up or giving off electrons or rearranging the inherent electrons. In some cases we see a combination of rearranging and taking up or giving off electrons. In the same manner as electron configurations at ground state only makes sense when looking at examples, these electron configurations also only makes sense when looking at real world examples.

Starting from the bottom with hydrogen, hydrogen comes with one electron. The 1s orbital requires 2 electrons, paired, to be stable. Helium has two electrons which is why it is stable, and unable to react with anything. For hydrogen you have two options, giving off the one electron it has, so there is no electron configuration, or take up one, so the electron configuration becomes 1s². In both cases, hydrogen ends up having a charge, either positive, written as H⁺, if it looses the electron, or H⁻, if it takes up an electron. The alternative to absorbing an electron and get a negative charge, is sharing the electron with another hydrogen, so each hydrogen delivers half a pair of electrons. Then they become H₂, and the electron pair becomes what is called a covalent bond, connecting the two hydrogen atoms. How bonds and orbitals relate will be addressed in another chapter.

Moving on to element no. 3, lithium. The electron configuration at the ground state is 1s²2s¹. Contrary to hydrogen, lithium cannot take up an electron and become Li⁻, 1s²2s². Instead it will give off the 2s electron and become Li⁺ with the electron configuration 1s². Like hydrogen, lithium can share electrons, forming pairs, e.g. Li₂, like H₂, and lithium oxide, Li₂O, where the two lithium atoms share electrons with oxygen, so that oxygen get the two unfulfilled 2p orbitals filled, and the two lithium get their 2s orbitals filled. By being bound to an element different from itself, the bonding becomes different from what you see for H₂ and Li₂ (this will be explained in the "chemical bonds" chapter), but the basic principle with the paired electrons is the same.

At the other end of the spectrum we have elements like chlorine. The electron configuration is [Ne]3s²3p⁵. Options are taking up one electron or giving off at least 5; 7 electrons to reach the electron configuration for the noble gas neon. For chlorine and the elements in that group, taking up one electron is the easiest solution. Chlorine thus becomes Cl⁻, having the electron configuration [Ne]3s²3p⁶.

The s and p orbitals are sensitive towards unpaired electrons and will attempt to get rid of them, but the d and f orbitals tolerate them. In some cases, unpaired electrons are preferred. Iron can be found as both Fe²⁺ and Fe³⁺. The electron configuration in the ground state is [Ar]3d⁶4s². Though the d electrons have the highest energy, Fe²⁺ is obtain by removing the 4s electrons (the outer electrons), so you get the configuration [Ar]3d⁶. In the d orbitals this is 1 par and four single electrons. Fe³⁺ which is actually the most common of the two ions, has given off an additional d electron, which gives the configuration [Ar]3d⁵ i.e. 5 unpaired electrons in the outer shell.

You might think that having 4 or 5 inpaired electrons in the outer shell, iron might have 4 or 5 covalent bonds, similar to oxygen's two unpaired electrons forming two covalent bonds, and hydrogen forming one. It cannot! Iron is what they call a transition metal, and these cannot form covalent bonds. Iron can form ion bonds and metal bonds, which are both fundamentally different from covalent bonds. The difference, and how they work, will be addressed in the "chemical bonds" chapter. In some educational material you may encounter the statement that the number of unpaired electrons in the outer shell is the same as the number of bonds. This is nonsens stemming from trying to dumb down the relationship between electrons and bonds so it would fit to the eight A ad B groups previously used for grouping the elements.

Instead of giving off, taking up or rearranging electrons in the orbitals, it is also possible to make hybrid orbitals. Carbon has the electron configuration [He]2s²2p². At first glance it looks like you should be able to give off 2 or 4 electrons, or take up 4 electrons, thereby getting C²⁺, C⁴⁺ or C⁴⁻, but none of these happens in real life. Instead carbon forms covalent bonds using the electrons. It is possible for carbon to form two covalent bonds with the orbitals at the ground state configuration, this is what happens when forming carbon monoxide (CO), but the most common, however, is for the s and p orbitals to merge. The four orbitals, one s and three p orbitals, merge to four sp₃ orbitals, each with one unpaired electron. The electron configuration is now [He]2sp₃⁴. The two options having 2 or 4 unpaired electrons, is the reason carbon can be observed having both 2 and 4 chemical bonds.