0.4 Electron shell model of an atom  (Page 4/6)

The striking observation is that the groups of elements appear “periodically” in the ranking of the elements by atomic number. Looking at the list in [link] , in each case we find, in order, a halogen, a noble gas, an alkali metal, and an alkaline earth metal, and this pattern repeats itself over and over again. This observation is called the Periodic Law, and it is the reason that the usual table of the elements is called the “Periodic Table,” which is arranged with the elements in each group placed together in columns.

Periodic Law: The chemical and physical properties of the elements are periodic functions of the atomic number.

This observation is very surprising! To see this, consider an analogy. Imagine we looked for a pattern in the grades of students in a class by where they like to sit. We would not be surprised to find a pattern. Perhaps, for example, the most attentive students sit in a group near the front of the class and make the highest grades. However, we would be very surprised if we were to rank the students in order of decreasing grades and discover that every tenth student (1 ^st , 10 ^th , 21 ^st , 31 ^st ) in the list sat in the first row, every other tenth student (2 ^nd , 12 ^th , 22 ^nd , 32 ^nd ) sat in the second row, and so forth. That would be very unexpected and very hard to explain. But we would look for a reason for the pattern. In a similar way, we have seen a surprising pattern in the behavior of the elements with atomic number, and we must look for a reason for that pattern.

Observation 2: ionization energies of the atom

We are now ready to use Coulomb’s Law, as discussed in the Foundation, to understand the attraction of the electrons flying about the nucleus to the positive charge of the nucleus. Recall that the attraction of two charges together depends on the sizes of the charges and the distance between them. The size of the charge on an electron is often called –e . In the case of an atom with atomic number Z , there are Z protons so the nuclear charge is +Ze . The attraction of an electron at distance r away from this nucleus is given by the potential energy in Coulomb’s Law:

$V(r)\mathrm{=}\frac{(+\text{Ze})(\mathrm{-}e)}{r}$

This means that an electron close to the nucleus would be more strongly attracted to the nucleus, because its potential energy is much more negative. A large negative potential energy means that we would have to add a lot of energy to the electron to remove it from the atom so that r could become large. This also means that an electron in an atom with a large atomic number, Z, would be more strongly attracted to its nucleus than an electron in another atom with a smaller atomic number.

We can actually observe the attractions of the electrons to the nucleus by measuring the amount of energy required to remove the electron from the atom. This energy is called the “ionization energy” of the atom because it is the energy required to take a neutral atom and turn it into a charged ion:

A (g) → A ⁺ (g) + e ^- (g)

In this chemical process, A is an atom, the (g) means that this atom is in the gas phase, and A ⁺ (g) is the same atom with one electron removed, leaving behind a positive charge. We call A ⁺ an ion. Think about how the ionization energy is related to the potential energy in Coulomb’s Law. For an electron to be removed from the atom, r must become very large so that the potential energy becomes essentially zero. If an electron began with a negative potential energy V(r) , we would have added at least this must energy to bring the potential energy up to zero. Therefore, a large negative V(r) would require a large ionization energy. We often call the ionization energy, IE, and it is typically measured in kiloJoules (kJ) per mole of atoms. At this point, we don’t need to worry about how this experiment is actually done.