LON-CAPA PeriodicTable

The Periodic Table

The periodic table is familiar to anyone who has had an introductory course in chemistry. It is a scheme wherein elements are organized into groups according to similarities in their physical and chemical properties. These similarities are a reflection of similarities in the electronic structures of the atoms within a particular group. The discussion that follows focuses on the periodic trends in atomic size and ionization energies to illustrate how our understanding of electronic structure developed. We will call upon Coulomb's Law to interpret and rationalize the data presented. Recall the form of this law:

In the situations that are discussed below q₁ represents the nuclear charge, i.e. the atomic number, q₂ is the charge on an electron, -1, while r stands for the atomic radius. F_c is the force of attaction between the nucleus and the electron.

Exercise 1 In a multi-electron atom, the nucleus exerts the least force on the electron that is closest to it. farthest from it.

We'll begin with a consideration of atomic size...

Atomic Size

Chemists view isolated atoms as small spherical particles. For most people, the radius of the sphere would be an indication of the atom's size. For chemists it's not so simple, neither theoretically nor experimentally. The theoretical problem arises from the Heisenberg uncertainty principle, which tells us that it is not possible to determine with certainty the position of an electron with respect to the nucleus of an atom. The best we can do is to talk about the probability of finding an electron within a certain volume of space that surrounds the nucleus of the atom. Experimentally it is difficult to obtain isolated atoms. Hydrogen, for example, exists as a dinuclear compound rather than a mononuclear atom. While we can measure the "size" of this dinuclear compound, the relationship between its "size" and the radius of the mononuclear atom is not obvious. Since we can't be precise, the meaning of the term atomic radius is necessarily fuzzy. By convention the atomic radius has come to be taken as the radius of a sphere that contains approximately 90% of the electron density of the atom. Figure 1 shows the sizes of a select group of elements arranged according to their positions in the periodic table, i.e. their atomic number. The atomic radius, in picometers, is given below the sphere that represents the atom. The fuzziness of the edges of the spheres is meant to imply the uncertainty inherent in discussions of the size of an atom.

Figure 1

Atomic Radii as a Function of Atomic Number

Before we consider the data in Figure 1, you may want to review your knowledge of the periodic table.

Exercise 2 Across a given row of the periodic table, the general trend is that the radii of the atoms decrease as their atomic numbers. Such a relationship between atomic number and atomic radius isa direct correlation. an inverse correlation.

According to Coulomb's Law, as the atomic number increases within a series of atoms, the nuclear attraction for electrons will also increase, thus pulling the electron(s) closer to the nucleus. The Coulombic attraction of the nucleus of an atom for its electrons is referred to as the electronegativity of the atom.

Exercise 3 Within a given group (column) of the periodic table, the general trend is that the radii of the atoms increase as their atomic numbers. Such a relationship between atomic number and atomic radius isa direct correlation. an inverse correlation.

At this point we have an apparent dichotomy. On the one hand there is a direct correlation between atomic size and atomic number, while on the other there is an inverse correlation between these two variables. Whenever you encounter a situation like this, you may be certain that there is another variable at play. You need more data. So let's look at ....

Ionization Energies

The ionization energy of an atom is the amount of energy required to separate an electron from the neutral atom. It is the energy needed to overcome the force of attaction, F_c, between the nucleus and the electron that is farthest from it. Equation 1 depicts the process in general terms. In this equation A represents any atom, while A⁺ stands for the ion that is produced when an electron, e^-, is removed from A.

Figure 2 presents a plot of ionization energies as a function of atomic number for the same elements shown in Figure 1.

Figure 2

Ionization Energies as a Function of Atomic Number

Exercise 4 Complete the following statement: Across a given row of the periodic table, the general trend is that the ionization energies of the atoms increase as their atomic numbers. Such a correlation between atomic number and ionization energy is direct inverse.

Exercise 5 Complete the following statement: Within a given group (column) of the periodic table, the general trend is that the ionization energies of the atoms decrease as their atomic numbers .

Let's think about what's involved in the measurement of the ionization energy of an atom. As Equation 1 indicates, the process requires the separation of an electron from the nucleus of an atom, i.e. the separation of a negatively charged particle from a positively charged particle. According to Coulomb's Law, the ionization energies are a function of two variables, the atomic number and the atomic radius. More importantly, these variables act in opposite directions on the ionization energies; an increase in atomic number should cause an increase in ionization energy, while an increase in atomic radius should result in a decrease. The actual value of the ionization energy for a given atom will depend upon the balance of these two factors.

Exercise 6 If q₂ represents the charge on the electron, then the ionization energies should increase as the values of q₁. The data in Figure 2 indicate that this is always true generally true never true

Before we proceed with our interpretation of the data in Figure 2, we need to take a closer look at Figure 1. Notice, for example, that as you go from oxygen to fluorine, i.e. from q₁ = 8 to q₁ = 9, the atomic radius decreases from 73 to 72 pm. Increasing the atomic number from 9 to 10 results in a further decrease in atomic size from 72 to 70 pm. However, when q₁ goes from 10 to 11, the atomic radius does not decrease, but rather jumps dramatically from 70 pm to 186 pm. This abrupt change in atomic size was one line of experimental evidence that led to the postulation of electron shells. This idea was put forth as a rationalization of the discrepency between the expectation that the atomic radius of sodium should be smaller than that of neon and the experimental fact that it is much larger. The idea is simple; electrons are arranged around the nucleus in shells, much like the layers of an onion. Each shell is identified by its principal quantum number, n. In neon, the 10th electron goes into a shell that has principal quantum number of 2. In sodium, the 11th electron goes into a shell that has n = 3. According to Bohr, the radius of an atom, i.e. the distance of the outermost electron from the nucleus, increases as the value of n increases.

Now let's return to our analysis of the data in Figure 2. Here, as you go from oxygen to fluorine, i.e. from q₁ = 8 to q₁ = 9, the ionization energy increases from 1314 to 1680 kJ/mol. This is consistent with the idea that the 9 protons in the nucleus of the fluorine atom exert a stronger force of attraction for the atom's outermost electron than the 8 protons in the oxygen atom exert on its outermost electron. This trend continues as you go from fluorine to neon; the ionization energy increases from 1680 to 2080 kJ/mol. But, when q₁ increases from 10 to 11, the ionization energy drops precipitously from 2080 to 496 kJ/mol! Once again we invoke the idea of electron shells in order to rationalize this result: The electron being removed from the neon atom is in a shell with n = 2, while the electron being removed from the sodium atom occupies the n = 3 shell.

If you look carefully at the data in Figure 2 you can also see evidence for the existence of electronic sub-shells. At first glance it is tempting to conclude that the data suggests three sub-shells, one containing two electrons and two others with three electrons each. However, other evidence indicates that only two sub-shells are warranted, the first containing two electrons and the second holding six. These are the familiar s and p sub-shells; 2s and 2p for the data set shown in red in Figure 2 and 3s and 3p for those in blue.

Finally, note that the red and blue data sets in Figures 1 and 2 each contain eight atoms. This is the basis for the filled shell rules. For an extensive treatment of the periodic table go to WebElements.

Additional Exercises