Chapter 3 – Atomic Structure and Properties

Introduction

The nuclear atom and quantum theory are the accepted theories for the atom. In this chapter, we demonstrate their utility by using them to explain trends in atomic properties.

3.1 Valence Electrons

Introduction

Most of the properties of an atom are related to the nature of its electron cloud and how strongly the electrons interact with the nucleus. In this section, we identify the electrons that are most important in determining atomic properties.

Prerequisites

• •
  2.7 Electron Configurations (Write electron configurations for atoms.)

Objectives

• •
  Distinguish between core and valence electrons.
• •
  Determine the number of valence electrons in an atom.
• •
  Write valence electron configurations of main group atoms.

3.1-1. Valence Electrons Video

3.1-2. Valence Electron Definition

The electrons in an atom can be divided into two groups:

• •
  Core electrons are the tightly bound electrons that are unaffected by chemical reactions. Core electrons reside in filled sublevels and form a spherical shell of negative charge around the nucleus that affects the amount of nuclear charge that the outermost electrons experience.
• •
  Valence electrons are those outermost electrons that dictate the properties of the atom and are involved in chemical bonding. The valence electrons are those in the outermost s sublevel and any unfilled sublevels.

3.1-3. Valence Electron Configurations of Main Group Elements

All of the elements in a group have the same number of valence electrons (Group number), and their valence electron configurations are the same except for the value of the n quantum number (the period). Thus, the periodicity of chemical properties is due to the periodicity of the valence electron configurations. The table shows the generic valence electron configurations of the elements in each group of the main group elements and the specific configurations of the second period.

Group	1A	2A	3A	4A	5A	6A	7A
Configuration	ns1	ns2	ns2np1	ns2np2	ns2np3	ns2np4	ns2np5
2nd Period Element	Li	Be	B	C	N	O	F
Configuration	2s1	2s2	2s22p1	2s22p2	2s22p3	2s22p4	2s22p5

Table 3.1: Valence Electron Configurations

3.1-4. Valence Electron Configurations of Transition Elements

The valence electron configuration of the first row transition elements has the form 4s²3d^b, where b is the position of the element in the d block. Cr and Cu are the two exceptions because they each promote one of their 4s electrons into the 3d sublevel to obtain half-filled and completely filled 3d sublevels. Zinc is often considered a transition element because of its location, but its d sublevel is full, and its chemistry is more like that of a Group 2A metal than a transition metal. Thus, its valence electron configuration is 4s², in keeping with its Group number of 2B. Similarly, Cu is 4s¹3d¹⁰, and the fact that it is a 1B element would lead you to think that its valence electron configuration should be 4s¹. However, unlike zinc, copper does use its d orbitals in bonding. Indeed, the most common ion formed by copper is the Cu²⁺ ion. Thus, copper's chemistry is dictated by its d electrons, and its valence electron configuration is 4s¹3d¹⁰.

3.1-5. Practice with Valence Electrons

Valence electrons and valence electron configurations are very important in chemistry. Practice determining the valence electron configurations for atoms and then check your answer by clicking on the element in the periodic table below.

1 1A

2 2A

3 3B

4 4B

5 5B

6 6B

7 7B

8 8B

9 8B

10 8B

11 1B

12 2B

13 3A

14 4A

15 5A

16 6A

17 7A

18 8A

H

He

Li

Be

B

C

N

O

F

Ne

Na

Mg

Al

Si

P

S

Cl

Ar

K

Ca

Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Cu

Zn

Ga

Ge

As

Se

Br

Kr

Rb

Sr

3.1-6. Core vs. Valence Electrons Exercise

3.1-7. Main Group Valence Configurations Exercise

3.1-8. Transition Metal Valence Configurations Exercise

3.1-9. More Valence Electron Configuration Exercises

3.2 Shielding and Effective Nuclear Charge

Introduction

In this section, you will learn how to predict the relative strengths with which the valence electrons interact with the nucleus.

3.2-1. Effective Nuclear Charge Video

3.2-2. Shielding and Effective Nuclear Charge

The nuclear charge experienced by an electron affects the size and energy of its orbitals, so it is an important factor in determining the properties of the valence electrons and orbitals. However, a valence electron is not attracted by the full positive charge of the nucleus because it is shielded by the other electrons, mainly the core electrons. The nuclear charge that is actually experienced by a valence electron is called the effective nuclear charge, Z_eff. The effective nuclear charge experienced by an electron is equal to the charge of the nucleus (Z) minus that portion of the nuclear charge that is shielded by the other electrons (σ). σ is the shielding of the other electrons. A valence electron is screened both by the core electrons and other valence electrons. However, core electrons are closer to the nucleus, so core electrons shield valence electrons better than do other valence electrons. This important fact will be used to explain the trends of atomic properties within a period.

3.2-3. Trends in Z_eff

Trends within a period: The charge of the nucleus increases by a full unit of positive charge in going from one element to the next in a period, but the additional electrons are valence electrons, which do not shield with a full negative charge. Consequently, effective nuclear charge increases going from left to right in a period. This effect is very important because it explains many trends within a period. Consider the following comparison of Li and F:

• 1
  Z = 3
  for Li, which is 1s²2s¹. Z_eff ~ 1 according to Figure 3.2. Thus, the two 1s electrons exert a shielding of
  σ ~ 3 − 1 = 2.
• 2
  Z = 9
  for F, which is 1s²2s²2p⁵, but Z_eff ~ 5. Thus, the shielding is σ ~ 9 – 5 = 4.

Although F has five more electrons than Li, they increase the shielding by only 2 (from 2 in Li to 4 in F). This is because they are valence electrons, which do not shield very well. Trends within a group: The shielding ability of the core electrons decreases as their n quantum number increases. As a result, the effective nuclear charge experienced by the valence electrons within a group increases with the n quantum number of the valence level. Consequently, effective nuclear charge increases going down a group. For example, the 2s electron on Li experiences an effective nuclear charge of ~1, while the 3s electron on Na experiences a charge of ~2, which shows that the

n = 2

electrons do not shield as well as the

n = 1

electrons. This effect opposes that of changing the n quantum number because increasing n increases the energy of the valence levels, but increasing the effective nuclear charge lowers the energy of the valence levels. The effect of increasing n is the more important because the energies of the valence levels do increase going down a group.

3.2-4. Effective Nuclear Charge Exercise

3.3 Relative Atomic Size

Introduction

Atoms are not hard spheres with well defined boundaries, so the term "atomic radius" is somewhat vague and there are several definitions of what the atomic radius is. Consequently, atomic radii are not measured directly. Rather, they are inferred from the distances between atoms in molecules, which can be readily determined with several techniques. However, a discussion of how atomic radii are defined requires an understanding of chemical bonding and the solid state, so a detailed discussion of the different types of radii and their values is postponed until Chapter 8. In this section, we restrict our discussion to trends in the relative sizes of atoms.

Prerequisites

• •
  1.8 Electromagnetism and Coulomb's Law
• •
  1.11 Dimitri Mendeleev and The Periodic Law
• •
  2.3 Bohr Model (Use the Bohr model to relate the size of an orbital to its n quantum number and atomic number.)

Objectives

• •
  Explain the periodicity in the size of valence orbitals.
• •
  Determine the relative sizes of atoms based on their positions in the periodic table.

3.3-1. The Bohr Model and Atomic Size

The size of the atom is given by the size of its valence electron clouds. Although the orbits of fixed radii suggested in the Bohr model are not correct, the conclusions of the model can still be used to gain a qualitative understanding of trends in atomic radii by substituting the effective nuclear charge for the atomic number in Equation 2.4 to obtain the following:

• •
  The average size of an orbital increases as its n quantum number increases.
• •
  The size of the electron cloud decreases as the effective nuclear charge it experiences increases.

3.3-2. Atomic Size

The size of an atom is defined by the size of the valence orbitals. Using the Bohr model as discussed above, we conclude that

• •
  atomic radii increase going down a group because the n quantum number of the outermost orbitals increases, and
• •
  atomic radii decrease going from left to right in a period because Z_eff increases.

Note that the atomic radii of H and Rb are

0.37 Å

and

2.11 Å,

respectively.

3.3-3. Atomic Size Exercise

3.4 Relative Orbital Energies

Introduction

The relative energy of the valence orbitals in an atom is an important characteristic of the atom as it dictates both properties of the atom and the manner and strength of its interaction with other atoms. Indeed, we will invoke relative orbital energies in making predictions about chemical processes throughout the remainder of this course. In this section, we use the Bohr model to predict the relative energies of the valence orbitals in some small atoms.

Prerequisites

• •
  1.8 Electromagnetism and Coulomb's Law
• •
  1.11 Dimitri Mendeleev and The Periodic Law
• •
  2.3 Bohr Model (Use the Bohr model to relate the energy of an orbital to its n quantum number and atomic number.)

Objectives

• •
  Determine the relative energies of electrons based on their n quantum number and the effective nuclear charge they experience.

3.4-1. Orbital Energies Video

3.4-2. The Bohr Model and Orbital/Electron Energy

The ease with which an electron is lost from an atom is given by how strongly the electron is bound to the atom, which, in turn, is given by the energy of the electron in the atom. We again use the conclusions of the Bohr model in a qualitative way to understand trends in valence electron energies by substituting the effective nuclear charge for the atomic number in Equation 2.5 to obtain Equation 3.2. E_x is the energy of a valence orbital on atom X, and n is the principle quantum number of its valence shell. While Equation 3.2 is only a very rough approximation, it is useful in demonstrating how the relative orbital energies of the valence electrons in the atoms of the first three periods are related. We conclude that

• 1
  The energy of an electron increases (becomes less negative and is bound less tightly) as its n quantum number increases.
• 2
  The energy of an electron decreases (becomes more negative and is bound more tightly) as the effective nuclear charge increases.

3.4-3. Relative Energies, an Example

We now determine the relative valence orbital energies of Li, C, and F as shown in Figure 3.4. We use the fact that they are each in the second period to get n and Figure 3.2 to obtain values of Z_eff and construct the table shown in Figure 3.4. We use Equation 3.2

E_x ∝ −

Zeff2

n2

and the values in the table to conclude the following.

• •
  The five 2p valence electrons of fluorine experience a highly positive effective nuclear charge of 5.2 and a very low n quantum number, so the value for

  Zeff2

  n2

  is quite large. Thus, the energy of the valence orbitals of fluorine is very low. Indeed, they are the lowest-energy valence orbitals of any atom. Nonmetals are all characterized by low-energy valence orbitals.
• •
  The two 2p electrons of carbon experience an effective nuclear charge of +3.3 and the same n quantum number as fluorine, so the value of

  Zeff2

  n2

  is less than that of fluorine. Thus, the valence electrons of carbon are not bound as tightly as those on fluorine and the carbon valence orbitals are higher in energy than those of fluorine. However, carbon is a nonmetal, and the energy of its valence orbitals is still relatively low.
• •
  Lithium is a metal, and its 2s valence electron experiences an effective nuclear charge of only +1.3, which produces a very low value for Z_eff squared over n squared. Consequently, the valence electron on a lithium atom is bound only weakly, and its valence orbital energy is quite high. Indeed, metals are all characterized by high-energy valence orbitals.

3.4-4. Predicting Relative Energy Exercise

3.4-5. Relative Valence Orbital Energies for Several Atoms

Before leaving our discussion of relative orbital energies, we add H (Z_eff = 1) and O (Z_eff = 4.5) to our energy diagram to obtain the following diagram that contains eight elements of the first three periods. We draw the following two conclusions based on the diagram:

• 1
  Orbital energies decrease (become more negative) going across a period because Z_eff increases. Thus,
  Li > C > O > F.
• 2
  Orbital energies increase (become less negative) going down a group because n increases. Thus,
  Si > C;
  S > O;
  and
  Cl > F.

3.4-6. Orbital Energy Exercise

3.4-7. Core vs. Valence Orbital Energies Exercise

The energies of the valence orbitals of all atoms lie in a relatively narrow range due to the periodicity in Z_eff and an increasing n quantum number. Core electrons, on the other hand, continue to drop in energy as the number of protons increases because they are not shielded very efficiently by the valence electrons. Thus, the valence 2p orbitals of oxygen are at lower energy than the valence 3p valence orbitals on sulfur because valence orbital energies increase going down a group, but the 2p electrons in oxygen are much higher in energy than the 2p electrons on sulfur because sulfur has 16 protons while oxygen has only eight.

3.5 Ionization Energy

Introduction

One of the properties of an atom that is important in dictating the chemical properties of the atom is the ease with which the atom loses one or more of its valence electrons. This property of an atom is given by the atom's ionization energy or ionization potential, the topic of this section.

Prerequisites

• •
  1.8 Electromagnetism and Coulomb's Law
• •
  1.11 Dimitri Mendeleev and The Periodic Law
• •
  2.3 Bohr Model (Use the Bohr model to relate the energy of an orbital to its n quantum number and atomic number.)

Objectives

• •
  Predict the relative ionization energies of atoms based on their positions in the periodic table or the relative energies of their occupied valence orbitals.

3.5-1. Ionization Energy Video

3.5-2. Ionization Energy and Orbital Energy

The ionization energy (IE) of an atom is the energy required to remove the highest energy electron. The ionization energy of lithium is 520 kJ/mol, which means that the electrons in a mole of lithium atoms can be removed by the input of 520 kJ. The ionization process is where ΔE = IE, the ionization energy. The energy change results because the energy of the electron in the initial state is different than in the final state. In the initial state, the electron is in an orbital of energy E_n, but in the final state, it is a free electron with no potential energy. The relationship between the ionization energy and the orbital energy is obtained as follows: Thus, IE = –E_n. The orbital energy of the highest energy electron can be approximated as the negative of the ionization energy of the atom. In the above discussion, we have considered the removal of only the highest energy electron, but as shown in the following, other electrons can also be removed by successive ionizations. Thus, the energy required to remove the first electron is the first ionization energy and that required to remove the second electron is the second ionization energy, and so forth. Consider the case of the metal M. The loss of an electron reduces the screening of the remaining electrons, so the remaining electrons experience greater nuclear charge and are more difficult to remove. Thus, each successive ionization energy is greater than the preceding. We use the term ionization energy to refer to the first ionization energy in the remainder of the chapter.

3.5-3. Putting Numbers to Orbital Energies

The energy required to remove one 2p electron from each atom in a mole of F atoms to produce a mole of F¹⁺ ions is 1681 kJ, so the ionization energy of fluorine is 1681 kJ/mol. In addition, 1681 kJ/mole are released in the reverse process, so we conclude that the 2p orbital energy is –1681 kJ/mol. Nonmetals are characterized by high ionization energies and low valence orbital energies because they have high effective nuclear charges. The ionization energy of carbon is 1086 kJ/mol, so the orbital energy of a 2p orbital in carbon is –1086 kJ/mol. The ionization energy of lithium is only 520 kJ/mol, so the orbital energy of its 2s orbital is –520 kJ/mol. The valence orbitals of metals are characterized by low ionization energies and high valence orbital energies because they have low effective nuclear charges.

3.5-4. Ionization Energy Trends

Ionization energy is the energy required to remove the highest energy electron from an atom, which can be estimated with the assumption that IE = –E_n; i.e., that the ionization energy equals the negative of the orbital energy of the electron. E_n can be estimated with Equation 3.2

E_x ∝ −

Zeff2

n2

, so we conclude that ionization energies

• •
  increase moving up a group due to the decrease in the n quantum number, and
• •
  increase from left to right in a period due to the increase in Z_eff.

This trend is shown in Figure 3.7, which shows the ionization energies of the atoms in order of atomic number. However, there are some apparent exceptions that arise because electron configurations in which sublevels are filled (Groups 2A and 8A) or half-filled (Group 5A) are unusually stable, so removing an electron from an element in one of these groups is more difficult and results in deviations from the expected periodicity. For example, the effective nuclear charge of B is greater than that of Be, but the ionization energy of Be is greater than that of B because the electron must be removed from a filled 2s sublevel in Be. Similarly, the ionization energy of N is greater than that of O because the 2p sublevel of N is half-filled. Summary

• •
  Metals are characterized by low effective nuclear charge, so they all have low ionization energies. Consequently, metals tend to lose electrons, and the farther to the left of the Periodic Table, the more easily the electrons are lost. Thus, the 1A elements lose their valence electron very easily. The ionization energy also decreases going down a family, so Cs (high n and low Z_eff) loses its valence electron so easily that it must be stored in oil because it gives up its 6s electron to water or oxygen when exposed to the air.
• •
  Nonmetals have high effective nuclear charges, so they have relatively high ionization energies. Thus, nonmetals do not lose their electrons very easily. Excluding the noble gases, F (low n and high Z_eff) has the highest ionization energy of any atom, which means that the valence electrons of fluorine are very tightly bound.

3.5-5. Ionization Energy Exercise

3.6 Electronegativity

Introduction

The electrons in a bond can lower their potential energy by residing closer to the atom in the bond that has the valence orbital at lower energy. The ability of an atom to attract the bonding electrons to itself is called its electronegativity (χ). Atoms are most electronegative when their valence orbitals are low in energy. Electronegativity is the topic of this section.

Prerequisites

• •
  1.8 Electromagnetism and Coulomb's Law
• •
  1.11 Dimitri Mendeleev and The Periodic Law
• •
  2.3 Bohr Model (Use the Bohr model to relate the energy of an orbital to its n quantum number and atomic number.)

Objectives

• •
  Predict the relative electronegativities of atoms based on their positions in the periodic table or the relative energies of their unfilled valence orbitals.
• •
  Explain the differences between metals and nonmetals that arise from the differences in their ionization energies and electronegativities.

3.6-1. Electronegativity Video

3.6-2. Electronegativity and Orbital Energy

Electronegativity (χ) is a measure of an atom's ability to attract bonding electrons, so electron density in a bond accumulates near those atoms with higher electronegativities. Bonding electrons reside in orbitals involving the valence orbitals of the atoms, especially those that are unfilled, and electrons seek to minimize their energy, so an atom that is highly electronegative is simply one whose valence orbitals, especially those that are unfilled, are low in energy. Consider the orbital energies of Li, C, and F shown in Figure 3.8. Li is a metal with a low Z_eff, so its orbital energy is high. The electron in it is readily lost (low ionization energy), but bonding electrons are not drawn to the high-energy orbital, so Li has a very low electronegativity. F is a nonmetal with a high Z_eff, so its orbital energy is low. Thus, it is very difficult to remove a 2p electron from F (high ionization energy), but bonding electrons are drawn to the low energy unfilled orbital, so F is highly electronegative. The 2p orbital energy of C is about halfway between the valence orbital energies of Li and F, and its electronegativity is also about half way between these two extremes in the period.

3.6-3. The Meaning of Electronegativity

The electronegativity difference between two atoms dictates the type of bond that forms between them. Refer to Figure 3.9 for the following discussion.

• 1
  The electronegativities of two fluorine atoms are identical, so the bonding electrons are shared equally by the two atoms. Bonds in which the bonding electrons are shared equally are called covalent bonds.
• 2
  Fluorine is more electronegative than carbon, so the bonding electrons in a C-F bond reside closer to the fluorine atom. The excess of electron density close to the fluorine atom gives it a partial negative charge. A Greek delta (δ) is used to indicate that it is only a partial charge as the carbon still experiences some of the negative charge of the bonding electrons.
• 3
  The electronegativity difference between Li and F is so great that the bonding electrons reside almost exclusively on the fluorine to give it a full negative charge. Bonds in which the bonding electrons are not shared but reside on one atom are called ionic bonds.

Ionic bonds are the topic of Chapter 4, and covalent bonds are discussed in Chapters 5 and 6.

3.6-4. Electronegativity Trends

We use the Bohr model to approximate the energy of the lowest energy empty orbital –E_n and conclude that

• •
  electronegativities decrease going down a group because n increases, which causes the orbital energies to increase, and
• •
  electronegativities increase going from left to right in a period because Z_eff increases, which causes the orbital energies to decrease (become more negative).

Consequently,

• •
  Nonmetals are characterized by high Z_eff, so their valence orbitals are low in energy. Consequently, nonmetals are highly electronegative (2.0 to 4.0).
• •
  Main group metals have low effective nuclear charges and are characterized by high energy valence orbitals. Thus, main group metals have very low electronegativities (0.7 to 1.5).

3.6-5. Late Metals

An exception to the above generality about the electronegativities of metals arises from the fact that d and f electrons do not shield very well because they contain two and three nodal planes, respectively. Therefore, the effective nuclear charge experienced by the valence orbitals in late metals (metals that lie on the right side of the Periodic Table) can be quite large. For example, Pb has 27 more protons and electrons than does Cs, but 24 of those electrons are d and f electrons, which do not shield the 27 additional protons very well. Thus, the 6p electrons in Tl and Pb experience relatively high Z_eff (12.25 and 12.39, respectively), which makes both of these metals fairly electronegative. Indeed, the electronegativity of Pb is much greater than that of Si even though they are in the same Group, and the valence orbitals in Pb have a much higher n quantum number. We conclude that due to their high effective nuclear charges, late metals have unusually high electronegativities (see Table 3.2), which impacts significantly on their chemical properties.

Metal	χ
Ag	1.9
Sn	2.0
Hg	2.0
Tl	2.0
Pb	2.3

3.6-6. Metals vs. Nonmetals

Metals are characterized by lower effective nuclear charges, so they have

• •
  relatively large atomic radii
• •
  lower ionization energies
• •
  lower electronegativities

Nonmetals are characterized by high effective nuclear charges, so they have

• •
  relatively small atomic radii
• •
  higher ionization energies
• •
  higher electronegativities

Thus, metals tend to lose electrons (low ionization energy), while nonmetals tend to gain electrons (high electronegativities).

3.6-7.Electronegativity Exercise

3.6-8. Orbital Energy and Atomic Properties Exercise

3.7 Magnetic Properties

Introduction

All magnetic properties are due to the magnetic fields caused by electron spin. However, no magnetic field is generated by paired electrons because the two different electron spins are opposed and their magnetic fields cancel. Consequently, the magnetic properties of an atom are due solely to its unpaired electrons. In this section, we give a brief introduction into the magnetic properties of atoms and materials.

Prerequisites

• •
  2.5 The Quantum Numbers (Explain the meaning of the m_s quantum number.)

Objectives

• •
  Explain the origin of magnetism.
• •
  Distinguish between paramagnetic and diamagnetic atoms.
• •
  Explain why magnetic atoms are not always magnetic materials.

3.7-1. Paramagnetism and Diamagnetism

Atoms with unpaired electrons are paramagnetic. Paramagnetic atoms align in magnetic fields due to the presence of the unpaired electrons. The more unpaired electrons an atom has, the more paramagnetic it is. Both Li and N have unfilled valence subshells, so both have unpaired electrons and are paramagnetic. N has three unpaired electrons while Li has only one, so N is more paramagnetic than Li. Atoms with no unpaired electrons are diamagnetic. Diamagnetic atoms do not align in magnetic fields because they have no unpaired electrons. Neither Be nor Ne has any unfilled valence shells, so both are diamagnetic.

3.7-2. Ferromagnetism

Paramagnetism and diamagnetism are atomic properties, not bulk properties. Thus, N and Li are paramagnetic atoms, but nitrogen gas and lithium metal are not magnetic because the unpaired electrons on the atoms pair with one another to form materials that are not magnetic. The magnetism you are familiar with is called ferromagnetism. It is a bulk property because it requires unpaired electrons in a material, not just in an isolated atom. Iron is the best known example. Fe atoms have four unpaired electrons, so Fe atoms are paramagnetic. When Fe atoms bond to form iron metal, there is electron pairing in the solid, but not all four electrons pair. Consequently, iron metal is magnetic and iron is a ferromagnet.

3.7-3. Paramagnetism Exercise

3.8 Exercises and Solutions

Select the links to view either the end-of-chapter exercises or the solutions to the odd exercises.

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