0.2 The structure of an atom  (Page 4/6)

Observation 3: ionization energies of the atoms

Each electron must move about the nucleus in an electrical field generated by the positive charge of the nucleusand the negative charges of the other electrons. Coulomb's law determines the potential energy of attraction of each electronto the nucleus:

where $(Z)e$ is the charge on the nucleus with atomic number $Z$ and $-e$ is the charge on the electron, and r is the distance from the electron to the nucleus. The potential energy ofan electron in an atom is negative. This is because we take the potential energy of the electron when removed to great distancefrom the atom (very large $r$ ) to be zero, since the electron and thenucleus do not interact at large distance. In order to remove an electron from an atom, we have to raise the potential energy fromits negative value to zero. According to Coulomb's law, we expect electrons closer to the nucleus to have a lower potentialenergy and thus to require more energy to remove from the atom.

We can directly measure how much energy is required to remove an electron from an atom. Without concerningourselves with how this measurement is made, we simply measure the minimum amount of energy required to carry out the following"ionization reaction":

Here, $A$ is an atom in the gas phase, and $A^{+}$ is the same atom with one electron $e^{-}$ removed and is thus an ion. The minimum energy required to perform the ionization is called the ionization energy . The values of the ionization energy for each atom in Groups I through VIII of the periodic table areshown as a function of the atomic number here .

This figure is very reminiscent of the Periodic Law, which states that chemical and physical properties ofthe elements are periodic functions of the atomic number. Notice that the elements with the largest ionization energies (in otherwords, the most tightly bound electrons) are the inert gases. By contrast, the alkali metals are the elements with the smallestionization energies. In a single period of the periodic table, between each alkali metal atom and the next inert gas atom, theionization energy rises fairly steadily, falling dramatically from the inert gas to the following alkali metal at the start of thenext period.

We need a model which accounts for these variations in the ionization energy. A reasonable assumption fromCoulomb's law is that these variations are due to variations in the nuclear charge (atomic number) and in the distance of theelectrons from the nucleus. To begin, we can make a very crude approximation that the ionization energy is just the negative ofthis attractive potential energy given by Coulomb's law. This is crude because we have ignored the kinetic energy and becauseeach electron may not have fixed value of $r$ .

Nevertheless, this approximation gives a way to analyze this figure . For example, from Coulomb's law it seemsto make sense that the ionization energy should increase with increasing atomic number. It is easier to remove an electron fromLithium than from Neon because the nuclear charge in Lithium is much smaller than in Neon. But this cannot be the whole picture,because this argument would imply that Sodium atoms should have greater ionization energy than Neon atoms, when in fact Sodiumatoms have a very much lower ionization energy. Similarly, although the ionization energy rises as we go from Sodium to Argon, theionization energy of Argon is still less than that of Neon, even though the nuclear charge in an Argon atom is much greater than thenuclear charge in a Neon atom. What have we omitted from our analysis?