Thinking it Through Problem 7.6

State the specific relationship that allows you to determine:
(a) which element has the larger atoms, Ge or S.
(b) which element is likely to have the larger first ionization energy, phosphorus or sulfur.
(c) which element is likely to have the more exothermic electron affinity, phosphorus or sulfur.

Understand the problem:

Variations of atomic properties with electronic structure are discussed in section 7.9 of the textbook. Atomic size, first ionization energies, and electron affinities are all properties that vary in a periodic fashion with respect to the location of the atom in the periodic table. The basic properties of atoms used to explain trends in atomic properties are the sizes of electron shells and the effective nuclear charge experience by valence shell electrons.

Represent the problem:

Atomic properties of atoms usually show an increase or decrease in numeric values as one moves from left to right in a period or top to bottom in a group in the periodic table. As one moves across a period additional valence electrons are added to the same shell but experience an increasing effective nuclear charge. Since electrons in the same shell are at approximately the same distance from the nucleus, effects across a period are dominated by the change in effective nuclear charge. Trends in atomic properties in columns or groups of the periodic table are dominated by the variation in size of shells. In a group the effective nuclear charge is essentially constant since the gain in nuclear charge moving from one row to the next is canceled by the gain in number of core electrons.

Lay out a plan of action:

(a) Atomic Size

Ge is a fourth period element with two 4p electrons placing it in the C group. S is a third period element with four 3p electrons. The use of atomic shell (principal quantum number) and effective nuclear charge as discussed above allow us to compare properties of atoms in the same row or column in the periodic table. Thus to compare the size of Ge in the fourth row, 14^th column with S in the third row, 16^th column we can compare Ge with Si and then compare Si with S. Both Si and Ge are 14^th column elements with +4 effective nuclear charges. Since Si in third period element it has a smaller atomic radius than does Ge a fourth period element. S has an even smaller atomic radius than Si since its effective nuclear charge is +6 with its valence electrons in the same shell with principal quantum number of 3. Comparing these three atoms with the cause for each noted below the inequality sign we conclude:

(b) First ionization energy

The first ionization energy is the energy needed to remove one electron from a gaseous isolated atom. The force that must be overcome to remove an electron from an atom is an electrostatic force between the negative charge on the electron and the positive nuclear charge screened by the core electrons, the effective nuclear charge. Electrostatic forces increase with increasing charge and decrease with distance. Thus for atoms in the same group with the same effective nuclear charge the size effect dominates and first ionization energies decrease from top to bottom as the radius of the shell holding the valence electrons increases. Within a period with electrons added to the same valence shell the charge effect dominates. First ionization energies increase from left to right in a period.

Phosphorus and sulfur are both third row elements. Since the effective nuclear charge on sulfur (+6) is larger than that on phosphorus (+5), sulfur has the larger first ionization energy.

(c) Electron affinity

Electron affinity, as defined in section 7.9 of the textbook, is the energy change that occurs when an electron adds to an isolated gaseous atom or ion. Usually the formation of an anion from a neutral atom is an exothermic process since the added electron experiences a net attractive force from the nucleus which dominates the repulsive forces with the atom's electrons. The trends in magnitudes of electron affinities follow those of ionization energies since both derive from the electrostatic force between the electron and the nucleus. In a group the size effect dominates with electron affinities decreasing from top to bottom. In a period the charge effect dominates and electron affinities increase from left to right.

Sulfur is expected to have a large electron affinity than phosphorus due to its larger effective nuclear charge for these third period atoms.

Verify your solution:

We can look up the values for these atomic properties in tables in chapter 7 and compare these with our predictions.

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