Volume 2
2.3. ELECTRONS IN ATOMS

Electron Shells • Electron Subshells. Orbitals. The 1st and 2nd Electron Shells: Populating the Orbitals with Electrons. The Aufbau Principle, the Pauli Principle, and Hund's Rule • The 3rd Shell. The Periodicity Comes from the Electron Configuration of the Outermost Shell • The 4th Electron Shell. The Tricks of d- and f-Orbitals • Exercises

2.3.1. Electron Shells. Chemists' interests are focused not on atomic nuclei but on electrons in atoms, and particularly those that are most distant from the nucleus. These electrons are called valence electrons, or outermost shell electrons. It is these electrons that are responsible for the formation of molecules from atoms through chemical bonding.

We already know that negatively charged electrons in atoms move around a positively charged atomic nucleus. We also know that the atomic number of an element is the total number of electrons (and, consequently, protons) an atom of that element has. Now we will learn how these electrons are arranged in atoms of various elements.

So, electrons are constantly and rapidly moving around an atomic nucleus. This movement, however, occurs only within certain orbit boundaries, characterized by specific distances from the nucleus. Like the planets of the Solar System revolve around the Sun while remaining on their particular orbits (Figure 2-16), the electrons in atoms move within their atomic orbits that are called electron shells or just shells.
Figure 2-16. The planets in the Solar System revolve around the Sun on particular well-defined orbits (source).


Electron shells are often called electron energy levels. Why this name? The negatively charged electrons are attracted to the positively charged protons in the nucleus. The electric force of these attractive interactions is stronger at shorter distances, stabilizing the electrons and lowering their energy. That is why it is said that electron shells that are closer to the nucleus are lower in energy than the more distant ones. Watch this video of a dog tied to a pole, running around like crazy. A dog on a much shorter leash (Figure 2-17) would not be able to run around as energetically. Likewise, an electron's energy is less when it is "tied" closer to the nucleus. Think: the dog = the electron, the leash = the attracting electric force, and the leash knot around the pole = the atomic nucleus.
Figure 2-17. A dog on a short leash (photo) cannot run around as energetically as a dog on a much longer leash (video).


Although the Solar System is a somewhat useful analogy to the atomic model, there are significant differences between the two.

First, the planet orbits are planar (Figure 2-16), meaning that the planets revolve around the Sun while remaining in one plane. In contrast, electron shells are 3-dimensional. Picture a hard boiled egg with the yolk removed. The shape of the solid egg white left might serve as a simplified representation of an electron shell. Within this shell the electrons quickly and chaotically move upwards, downwards, sideways, and in all possible directions.

Second, most drawings of atoms conventionally show well-defined boundaries of electron shells, such as in Figure 2-8. Similarly, the white of a hardboiled egg has well-defined inner and outer boundaries. However, the boundaries of an electron shell are blurred. Any graphic representation of an electron shell only shows the 3-dimensional areas where the probability of finding an electron is the highest.

Third, each orbit of the Solar System carries only one planet. In contrast, electron shells can accommodate more than one electron. The maximum number of electrons the nth shell can house is calculated by the formula 2n2. The 1st shell can hold up to 2 electrons, the 2nd shell up to 8 electrons, the 3rd shell 18 electrons, and so on.

2.3.2. Electron Subshells. Orbitals. The 1st and 2nd Electron Shells: Populating the Orbitals with Electrons. The Aufbau Principle, the Pauli Principle, and Hund's Rule. Each electron shell comprises subshells, which, in turn, consist of orbitals. The electron system of an atom could be compared to a multistory hotel building. On each floor of the hotel are located rooms of different type (class). All rooms within each class are identical, while being different from the rooms of another class. So, we think this way:

- The hotel building = atom
- Each floor of the building = electron shell
- Each set of identical rooms (of the same class) within a floor = electron subshell
- Each room, regardless of its type = orbital
- Each hotel guest = electron

Let us consider the first two electron shells (floors) with all of the rooms (orbitals) depicted as shapes (Figure 2-18).
Figure 2-18. Schematic representation of the first two electron shells (n = 1 and 2). The dot in the center of the orbitals depicts the nucleus.


Our "1st floor" is the first electron shell (n = 1), which is the lowest in energy (closest to the nucleus). This "floor" (shell) has only one "room" (orbital), which is spherical in shape. In Figure 2-18, this orbital drawn in red. All spherical orbitals are called s-orbitals.

While there is only one "room" (orbital) and, consequently, only one "type of room" (one subshell) on the "1st floor" (1st shell), the "2nd floor" (2nd shell) features a total of four "rooms" (four orbitals) of two different "classes" (two subshells). All four orbitals of the 2nd shell (n = 2) are drawn in blue in Figure 2-18. One of the four is another spherical orbital (s-orbital). The other three orbitals of the 2nd shell are slightly higher in energy and have a "dumbbell" shape. Orbitals of this shape are referred to as p-orbitals. All three p-orbitals are identical, except for their orientation in space. As shown in Figure 2-18, the three are perpendicular to one another.

There is an s-orbital in the 1st shell and there is another s-orbital in the 2nd shell (Figure 2-18). To make a distinction between the two, the electron shell number is placed before the letter depicting the shape. Thus, s-orbitals of the 1st and 2nd shells are represented as 1s and 2s, respectively. The p-orbitals of the 2nd shell are denoted as 2p.

Let us now populate the first two electron shells by placing electrons in the orbitals, one by one. (Protons and neutrons will be conceptually added to the nucleus automatically to maintain electroneutrality of the atom and stabilize the nucleus.) The process of filling electron shells with electrons is governed by three rules: the aufbau principle, the Pauli principle, and Hund's rule.

1. The aufbau principle (aufbau is the German for "building up") states that to gain maximum stability, electrons populate the lowest available energy shells first.

2. As follows from the Pauli principle, each orbital can accommodate up to only two electrons. (Up to two "guests" per "room".) Without going into detail, two electrons can occupy the same orbital only if they have opposite spins. In oversimplified terms, an electron spins on its axis like planets spin on theirs. Two electrons have opposite spins if they spin in opposite directions, such as clockwise and counterclockwise (Figure 2-19).
Figure 2-19. Two electrons occupying the same orbital have opposite spins.


3. Hund's rule states that all identical orbitals within a given subshell must be occupied by one electron before they can be occupied by two electrons. We will clarify this soon.

Now we can start putting electrons in the shells. To abide by the aufbau principle, our first electron goes into the lowest energy shell that has only one orbital, 1s. What we have as a result is the atom of hydrogen (Figure 2-20), the first element of the periodic table.
Figure 2-20. An atom of hydrogen features only one electron, located in the lowest lying 1s orbital.


Adding one more electron (and one proton and two neutrons) gives rise to the atom of helium (He), element number 2 of the periodic table (Figure 2-21).
Figure 2-21. A helium atom has two electrons on 1s orbital.


Helium has an atomic radius of 0.31 Å and is the smallest atom known. [The symbol Å is for the angstrom, a unit of length; 1 Å = 10−10 m.] The atomic radius of hydrogen is considerably larger, 0.53 Å. Why? Because the attracting electric force (Figure 2-11) between a negatively charged object and a positively charged object is proportional to the value of each charge. A hydrogen atom has only one electron (-1) and one proton (+1), whereas helium has two electrons (-2) in the same 1s orbital and two protons (+2). The stronger attraction between the larger charges entails the contraction, which makes the atom of helium smaller than the atom of hydrogen (Figure 2-22).
Figure 2-22. A helium atom is smaller in size than a hydrogen atom due to the contraction caused by stronger attraction forces between the larger opposite charges in helium relative to hydrogen.


By placing two electrons in the 1s orbital we complete the first electron shell that has only one subshell consisting of only one 1s orbital. Remember that no orbital can house more than two electrons (no more than two guests per room). Our third electron therefore has to go into the 2s orbital, and so does the fourth to give rise to the atoms of lithium (Li) and beryllium (Be), respectively (Figure 2-23). Find Li and Be in the periodic table and note that by starting to fill the 2s orbital, we start a new period.
Figure 2-23. Distribution of electrons in the atoms of lithium (Li) and beryllium (Be).


The next, fifth electron is accommodated by one of the three vacant 2p orbitals. As these three orbitals are identical, the electron can be placed in any one of them to generate the atom of boron (B). In Figure 2-24, the 5th electron is placed in the 2p orbital that is perpendicular to the plane of the drawing. It would be as correct to put this electron in either of the other two dumbbell-shaped 2p orbitals positioned horizontally or vertically in the sketch plane.
Figure 2-24. The 5th electron goes into one of the three 2p orbitals to produce the boron (B) atom.


When adding the next, 6th electron to our model we face a dilemma. It is clear that the electron has to go into one of the three 2p orbitals. But, should it go into the one that has one electron already, or one of the two empty ones? At this point, Hund's rule comes into play. Hund's rule states that all identical orbitals within a given subshell must be occupied by one electron before they can be occupied by two electrons (Figure 2-25). In other words, no 2p orbital can have two electrons before each of the other two 2p orbitals has at least one electron. It is not uncommon to compare Hund's rule with the way people are inclined to occupy seats on a train or bus (Figure 2-26). Double seats get doubly occupied only after they are all taken by a single passenger.
Figure 2-25. Incorrect (left) and correct (right) placement of an electron into the 2p subshell already bearing one electron (Hund's rule). The image on the right shows the distribution of electrons in the atom of carbon.
Figure 2-26. Figure 2-26. Double seats on a bus tend to be singly occupied before getting doubly occupied (source). Likewise, identical atomic orbitals are all first filled with one electron before getting occupied by two electrons.


To obey Hund's rule, the next element, nitrogen (N), has one electron in each of the three 2p orbitals (Figure 2-27). Placing the next 3 electrons into the already singly occupied 2p orbitals to produce atoms of oxygen (O), fluorine (F), and neon (Ne) is a no-brainer (Figure 2-28).
Figure 2-27. Electron distribution in the nitrogen (N) atom. Note that all three 2p orbitals are singly occupied in accord with Hund's rule.
Figure 2-28. Electron distribution in the atoms of (left to right) oxygen (O), fluorine (F), and neon (Ne).


Up to this point, we have used orbital shape drawings to describe the electron configuration of an atom, the way electrons are distributed in the atomic shells and subshells. There are two more widely used alternative ways to show how electrons are arranged in an atom. One is to write the occupied orbitals in the order of their increasing energy with the number of electrons in each subshell as a superscript. By this method, the electron configuration for the first 10 elements of the periodic table is as follows.
H (hydrogen) ------- 1s1

He (helium) --------- 1s2

Li (lithium) ----------- 1s2 2s1

Be (beryllium) ------ 1s2 2s2

B (boron) ------------- 1s2 2s2 2p1

C (carbon) ----------- 1s2 2s2 2p2

N (nitrogen) --------- 1s2 2s2 2p3

O (oxygen) ----------- 1s2 2s2 2p4

F (fluorine) ----------- 1s2 2s2 2p5

Ne (neon) ------------- 1s2 2s2 2p6
The electron configuration of an atom is also often represented as a set of boxes, each box symbol portraying one atomic orbital. These boxes are used in place of the orbital shapes (Figure 2-29).
Figure 2-29. A way to express the electron configuration of an atom is to draw boxes in place of orbital shapes. Compare with Figure 2-18.


The electrons occupying the orbitals are drawn as vertical arrows inside the boxes. Figure 2-30 illustrates this method for the elements of the 1st and 2nd periods. The opposite direction arrows inside the boxes symbolize electrons of opposite spins.
Figure 2-30. Figure 2-30. Orbital box diagrams depicting electron configurations of atoms of the 2nd period, hydrogen (H) through fluorine (F).


2.3.3. The 3rd Shell. The Periodicity Comes from the Electron Configuration of the Outermost Shell. The second period of the periodic table ends with neon (Ne), a noble gas. The electron configuration of Ne, 1s2 2s2 2p6, shows that all ten available orbitals of the 1st and 2nd electron shells are completely filled (Figure 2-31). To continue populating our "multistory building" (atom) with "tenants" (electrons), we now need to use the "rooms" (orbitals) of the next, "3rd floor" (3rd electron shell).
Figure 2-31. In the atom of neon (Ne), both the 1st and 2nd electron shells are completely filled with electrons.


The filling of the s and p orbitals of the 3rd shell (n = 3) with electrons takes place in exactly the same manner as that of the 2nd shell. The first two electrons go to the lowest energy orbital of the 3rd shell, 3s, which is farther away from the nucleus than any of the orbitals of the 2nd shell, let alone the 1st shell (Figure 2-32).
Figure 2-32. A shape model displaying 1s, 2s, 2p, and 3s atomic orbitals (source).


As shown in Figure 2-33, sodium (Na), the first element of the 3rd period, has the electron configuration 1s2 2s2 2p6 3s1. The next electron goes into the same 3s orbital to give an atom of magnesium (Mg), 1s2 2s2 2p6 3s2. After that, the 3p orbitals begin to get filled. The first 3p element is aluminum (Al; 1s2 2s2 2p6 3s2 3p1), see Figure 2-33.
,Figure 2-33. Electron configurations of the first three elements of the 3rd period, sodium (Na), magnesium (Mg), and aluminum (Al).


Now it is your turn to do the job. Finish the filling of the 3p orbitals for the next five elements: Si, P, S, Cl, and Ar. Draw the electron configuration of these elements following Figure 2-33 by example. Also try to sketch orbital shapes for all elements of the 3rd period. In doing so, consider drawing just the outermost 3s and 3p orbitals while omitting the inner 1s, 2s, and 2p orbitals in order to avoid overcrowded and confusing images.

We are now in possession of enough information to draw an extremely important conclusion, as follows.
Chemical properties of an element are determined by the electron configuration of its outermost electron shell or, in other words, by its valence electrons.
To see how we can arrive at this conclusion, we will take a closer look at the elements of the 2nd and 3rd periods and look for correlations between their electron configuration and chemical properties. (We are not considering the 1st period because it contains only two elements, H and He, which is insufficient for our analysis.)

First, let us analyze the horizontal rows (periods). All elements of the 2nd period (Figure 2-34) differ from one another in terms of chemical behavior. This dissimilarity is consistent with the different outermost electron shell configuration for each of these elements (shown red in Figure 2-34), but not with the inner shell configuration which is the same for all of them (1s2).
Figure 2-34. The 2nd period of the periodic table.


The same pattern is observed for the elements of the 3rd period (Figure 2-35). Again, these elements differ from one another in terms of both chemical behavior and the number of valence electrons, while having an identical inner electron shell configuration (1s2 2s2 2p6).
Figure 2-35. The 3rd period of the periodic table.


The considerations above indicate that it is the outermost electron shell configuration of an element that controls its chemical properties. This inference is nicely confirmed by comparison of the elements of the 2nd and 3rd periods within each group (vertical columns in Figure 2-36). The two alkali metals Li and Na (1st column in Figure 2-36) have very similar properties and the same electron configuration of the outermost shell, 2s1 and 3s1, respectively. The same is true for the pairs of the alkaline earth metals Be (2s2) and Mg (3s2), halogens F (2s2 2p5) and Cl (3s2 3p5), noble gases Ne (2s2 2p6) and Ar (3s2 3p6), carbon (2s2 2p2) and silicon (3s2 3p2), etc. Table 2 summarizes our analysis that leads us to the conclusion that it is the outermost, not inner electron shell that determines chemical properties of an element.
Figure 2-36. Elements within the same group exhibit similar chemical properties and feature the same configuration of the outermost electron shell.


Table 2 summarizes our analysis that leads us to the conclusion that it is the outermost, not inner electron shell that determines chemical properties of an element.


Table 2. Chemical properties of elements as a function of their outermost electron shell configuration.
We have learned how electrons populate orbitals for the elements of the 1st, 2nd, and 3rd periods of the periodic table. Continue reading to see what happens if we keep adding electrons to fill the next shells.

2.3.4. The 4th Electron Shell. The Tricks of d- and f-Orbitals. The last element we considered was argon (Ar). The electron configuration of argon, 1s2 2s2 2p6 3s2 3p6, shows that the outermost shell 3s and 3p orbitals are completely filled with electrons. Consequently, the next electron goes to the 4s orbital to give rise to an atom of potassium (K; 1s2 2s2 2p6 3s2 3p6 4s1), the element that starts the 4th period. The similarity of the electron configuration of the outermost shell of K (4s1) with those of Li (2s1) and Na (3s1) suggests that potassium should have chemical properties similar to those of Li and Na. It does indeed.

Adding one more electron to the electron configuration of potassium gives rise to calcium (Ca, 1s2 2s2 2p6 3s2 3p6 4s2), a typical member of group 2 comprising the alkaline earth metals.

Given the trend so far, one might think that the next electron would go into a 4p orbital. But this is not the case. After the 4s orbital has been filled, it is not 4p but 3d orbitals that start hosting incoming electrons. There are five d orbitals within a given shell. Consequently, filling the 3d orbitals with electrons one by one gives rise to ten new elements, from scandium (Sc) through zinc (Zn). These elements are called d-block elements because their highest energy electrons are located in d-orbitals. They are also conventionally called transition metals because they all exhibit metallic properties while representing a transition between elements bearing valence electrons in the s orbital and those in the p orbitals of the same shell.

As mentioned above, the maximum number of electrons the nth shell can accommodate is calculated by the formula 2n2. Hence the 3rd shell can house 2 x 32 = 18 electrons. Of these 18 electrons, 2 and 6 are hosted by the 3s and 3p orbitals, respectively. The remaining 10 electrons occupy the five 3d orbitals.

The question arises as to why is it that the d orbitals of the 3rd shell are filled with electrons after, not before the s orbital of the 4th shell? Figure 2-37 gives an answer to this question. While belonging to the 3rd shell, the 3d orbitals are higher in energy than the 4s orbital. This is an interesting feature of our "multistory hotel for electrons". We already know that the p-orbitals are higher in energy than the s-orbital of the same shell. The d-orbitals are higher in energy than the p-orbitals of the same shell and, as it turns out, the s-orbital of the next shell up as well.
Figure 2-37. Orbital energy diagram showing that the 3d orbitals are higher in energy than the 4s orbital.


Find scandium (Sc) and zinc (Zn), the first and the last 3d-block elements, in the periodic table. Figure 2-38 displays the electron configuration of atoms of these two elements as well as two more transition metals (Mn and Ni) located in between.
Figure 2-38. The electron configuration of Sc, Mn, Ni, and Zn as representatives of the 3 d-block elements.


After zinc (Zn), the 4p orbitals begin to get populated with electrons to give the next six elements, as follows.

Gallium (Ga): 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p1 (outer shell 4s2 4p1, analog of B and Al)

Germanium (Ge): 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p2 (outer shell 4s2 4p2, analog of C and Si)

Arsenic (As): 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p3 (outer shell 4s2 4p3, analog of N and P)

Selenium (Se): 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p4 (outer shell 4s2 4p4, analog of O a nd S)

Bromine (Br): 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5 (outer shell 4s2 4p5, analog of F and Cl)

Krypton (Kr): 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 (outer shell 4s2 4p6, analog of He and Ne)

The general order of filling atomic orbitals is:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, etc.

Actually, the "etc." at the end of the order line above is probably not too self-evident. After the 6s orbital has been filled with two electrons and the 5d orbital with one electron, another peculiar thing happens. The electrons start populating the 4f orbitals to form the f-block elements or lanthanides. The lanthanides (La through Lu) as well their heavier analogs actinides (Ac through Lr) are conventionally placed as two separate rows underneath the main body of the periodic table. This is done to make the periodic table more compact, as otherwise it would look like this. Overwhelmed? Relax! In our course, we will not deal with any f-block elements and will only touch on selected d-block elements. Nevertheless, it is worth taking a glance at Table 3 summarizing the electron capacity of the first four electron shells and their orbital details.


Table 3. The number of electrons the nth electron shell can accommodate for n = 1, 2, 3, and 4.
2.3.5. Exercises.

1. Electrons in atoms (a) revolve around an atomic nucleus on planar orbits; (b) rotate clockwise and counter-clockwise on 3-dimensional orbits that always have a spherical shape; (c) move chaotically within particular spaces that are called orbitals. Answer

2. Compared to an electron in the 1s orbital, an electron in the 2s orbital of the same atom is less attracted by the nucleus and, consequently, has less energy. True or false? Answer

3. Atomic orbitals have sharply defined physical boundaries. True or false? Answer

4. Each single atomic orbital can accommodate (a) up to two electrons; (b) different number of electrons, the capacity being 2, 6, and 10 electrons for s-, p-, and d-orbitals, respectively; (c) only one electron, in accord with the Pauli principle. Answer

5. An orbital can accommodate two electrons only if the two (a) have the same spin; (b) have opposite spins; (c) have no spin. Answer

6. Hund's rule states that identical orbitals within the same shell cannot have two electrons before each of them has one electron. True or false? Answer

7. Draw shapes of an s-orbital and a p-orbital. Answer

8. Draw shapes of all five d-orbitals and all seven f-orbitals. Answer

9. Every electron shell has three p-orbitals. True or false? Answer

10. The three p-orbitals of a given electron shell are (a) identical in terms of energy and shape; (b) perpendicular to one another; (c) coplanar (located in the same plane); (d) identical in shape but different in energy; (e) higher in energy than the s-orbital of the same shell; (f) lower in energy than the s-orbital of the same shell. Answer

11. Write the electron configuration of all elements of the 1st, 2nd, and 3rd periods of the periodic table as a sequence of atomic subshell labels 1s2 2s2 2p… etc. Example: H, 1s1; He, 1s2; Li, 1s2 2s1; Be, 1s2 2s2; B, 1s2 2s2 2p1; etc.

12. Draw orbital box diagrams for H, He, Be, C, N, F, Na, Al, P, Cl, Ar, K, Ca, Fe, Zn, Ga, Se, and Br. [Tip: See Figures 2-30, 2-31, 2-33, and 2-38]

13. Would you expect an oxygen atom to be larger or smaller in size than a carbon atom? Why? Answer

14. Formulate and comment on the aufbau principle.

15. Elements of (a) the same group exhibit similar chemical properties because they have the same electron configuration of the inner shell; (b) the same period have different properties because they have different electron configurations of the outermost shell; (c) the same period have similar chemical properties because they have the same electron configuration of the inner shells; (d) the same group have similar chemical properties because they have the same electron configuration of the outermost shell. Answer