02/14 Atomic Structure and the Periodic Table

Atomic Theory and the Structure of Matter

Modern atomic theory developed as experiments revealed that atoms are not indivisible spheres. An atom consists of a small, dense nucleus surrounded by an electron cloud. The nucleus contains positively charged protons and neutral neutrons, while negatively charged electrons occupy regions of space around the nucleus.

Nearly all the atom’s mass is concentrated in the nucleus, but nearly all its volume is associated with the electron cloud. An atom has a diameter of about $10^{-10}\,\mathrm{m}$, while its nucleus is approximately $10^{-15}\,\mathrm{m}$ in diameter.

The identity of an element is determined by its number of protons. Chemical reactions usually rearrange electrons while leaving the nuclei unchanged, so ordinary chemical reactions do not change one element into another. Atoms combine in definite ratios because their electrons interact in predictable ways.

Quantum mechanics provides the current model of electron behavior. Electrons do not move in fixed circular paths. Instead, an orbital is a mathematical region in which an electron is likely to be found. Each orbital can contain no more than two electrons with opposite spins.

Takeaway: The nucleus determines most of an atom’s mass and identity, while the electron arrangement largely determines chemical behavior.

Subatomic Particles, Isotopes, and Ions

The three major subatomic particles differ in charge, mass, and location:

• A proton, $p^+$, has relative charge $+1$, approximate relative mass $1$, and is located in the nucleus.

• A neutron, $n^0$, has charge $0$, approximate relative mass $1$, and is located in the nucleus.

• An electron, $e^-$, has charge $-1$, approximate relative mass $1/1836$, and occupies the electron cloud.

The atomic number is the number of protons:

The mass number is the number of protons plus neutrons:

Therefore, the number of neutrons is $A-Z$. For example, ${}^{23}_{11}\mathrm{Na}$ contains $11$ protons and $23-11=12$ neutrons. If the atom is neutral, it also contains $11$ electrons.

For an ion, use the charge to determine the electron count:

Thus, $\mathrm{Mg^{2+}}$ has $12$ protons and $10$ electrons, while $\mathrm{Cl^-}$ has $17$ protons and $18$ electrons. A cation forms by losing electrons, and an anion forms by gaining electrons.

Takeaway: Identify the element from protons, calculate neutrons from mass number, and adjust the electron count according to charge.

Isotopes and Average Atomic Mass

Isotopes are atoms of the same element with different numbers of neutrons. For example, carbon-12 and carbon-13 each contain $6$ protons, but carbon-12 has $6$ neutrons and carbon-13 has $7$.

The atomic mass shown on a periodic table is usually a weighted average of the naturally occurring isotope masses:

Convert each percentage to a decimal before using it. Suppose an element has the following isotopes:

• mass $10.0129\,\mathrm{u}$, abundance $19.9\%$;

• mass $11.0093\,\mathrm{u}$, abundance $80.1\%$.

The calculation is:

The result is closer to $11\,\mathrm{u}$ because the second isotope is more abundant. The atomic mass unit, $\mathrm{u}$, is convenient for expressing the masses of individual atoms.

Takeaway: Isotopic composition determines the periodic-table average, so the average is pulled toward the mass of the more abundant isotope.

Energy Levels and Electron Configurations

Electrons occupy principal energy levels identified by $n=1,2,3,\ldots$. Each principal level contains subshells:

• The $s$ subshell has one orbital and holds a maximum of $2$ electrons.

• The $p$ subshell has three orbitals and holds a maximum of $6$ electrons.

• The $d$ subshell has five orbitals and holds a maximum of $10$ electrons.

• The $f$ subshell has seven orbitals and holds a maximum of $14$ electrons.

A principal energy level can hold a maximum of:

The third level therefore holds a maximum of $2(3)^2=18$ electrons.

Three rules guide electron placement:

1. The Aufbau principle places electrons in available orbitals of lower energy before higher-energy orbitals.

2. The Pauli exclusion principle limits each orbital to two electrons with opposite spins.

3. Hund’s rule places electrons singly in equal-energy orbitals before pairing them.

The usual filling sequence is:

Examples of configurations include:

• Hydrogen, $Z=1$: $1s^1$.

• Carbon, $Z=6$: $1s^2\,2s^2\,2p^2$.

• Oxygen, $Z=8$: $1s^2\,2s^2\,2p^4$.

• Sodium, $Z=11$: $1s^2\,2s^2\,2p^6\,3s^1$, or $[\mathrm{Ne}]3s^1$.

Some transition metals have exceptions to the simplest filling order. Chromium is commonly written as $[\mathrm{Ar}]3d^5 4s^1$. When transition-metal cations form, electrons are generally removed from the highest principal energy level first. Thus, $\mathrm{Fe}$ is $[\mathrm{Ar}]3d^6 4s^2$, while $\mathrm{Fe^{2+}}$ is $[\mathrm{Ar}]3d^6$.

Takeaway: Build configurations by electron count, orbital energy, and the three placement rules; then verify that all superscripts add to the correct number of electrons.

Valence Electrons and Periodic Organization

The periodic table is arranged by increasing atomic number. Its horizontal rows are periods, and its vertical columns are groups. Elements in the same group often have similar chemical properties because they have related valence-electron configurations.

For main-group elements, common patterns include:

• Group 1: $ns^1$, often forming $1+$ ions.

• Group 2: $ns^2$, often forming $2+$ ions.

• Group 13: $ns^2np^1$, often forming $3+$ compounds.

• Group 14: $ns^2np^2$, often sharing electrons.

• Group 15: $ns^2np^3$, often forming three bonds or gaining three electrons.

• Group 16: $ns^2np^4$, often forming $2-$ ions or two bonds.

• Group 17: $ns^2np^5$, often forming $1-$ ions.

• Group 18: $ns^2np^6$, generally showing low chemical reactivity.

The table is also divided into blocks according to the subshell being filled. The $s$ block is mainly groups $1$ and $2$, the $p$ block is groups $13$ through $18$, the $d$ block contains transition elements, and the $f$ block contains the lanthanides and actinides.

Hydrogen is placed in group $1$ because it has one electron, but it is a nonmetal and does not behave like an alkali metal in every situation. Helium is placed in group $18$ because its first energy level is filled and especially stable, even though its configuration is $1s^2$.

Takeaway: Group position and valence-electron configuration provide a first prediction of common ion charges, bonding patterns, and reactivity.

Periodic Trends and Their Causes

Periodic properties result from the interaction of nuclear charge, electron shielding, electron–electron repulsion, and the principal energy level of the outer electrons.

Effective nuclear charge can be approximated by:

Across a period, proton number increases while added electrons generally enter the same principal energy level. Effective nuclear charge therefore usually increases. Down a group, additional energy levels increase both distance from the nucleus and shielding.

These ideas explain the major trends:

• Atomic radius: generally decreases from left to right and increases from top to bottom. Sodium is larger than chlorine in period $3$, while potassium is larger than sodium in group $1$.

• Ionic radius: cations are generally smaller than their neutral atoms because electrons are removed, while anions are generally larger because added electrons increase repulsion. Thus, $r(\mathrm{Na^+})<r(\mathrm{Na})$ and $r(\mathrm{Cl^-})>r(\mathrm{Cl})$.

• First ionization energy: generally increases across a period and decreases down a group. It is the energy required for $\mathrm{X(g)\rightarrow X^+(g)+e^-}$. A large effective nuclear charge and small radius make an electron harder to remove.

• Electron affinity: describes the energy change for $\mathrm{X(g)+e^-\rightarrow X^-(g)}$. Halogens often have favorable electron affinities, although subshell stability and electron repulsion produce exceptions.

• Electronegativity: generally increases upward and to the right. It describes how strongly an atom in a bond attracts shared electrons.

• Metallic character: generally increases downward and to the left. Metals more readily lose electrons, nonmetals more often gain or share them, and metalloids have intermediate properties.

For an isoelectronic series, each species has the same number of electrons. The species with more protons is smaller because its electrons experience greater nuclear attraction. The approximate largest-to-smallest order for $\mathrm{O^{2-}}$, $\mathrm{F^-}$, $\mathrm{Ne}$, $\mathrm{Na^+}$, and $\mathrm{Mg^{2+}}$ is the order listed.

Takeaway: Across a period, increasing effective nuclear charge usually pulls electrons inward; down a group, added energy levels and shielding usually make atoms larger and their outer electrons easier to remove.

Atomic Structure, Bonding, and Reactivity

Valence-electron arrangements connect atomic structure to ions, bonds, and reactivity.

Sodium has the configuration $\mathrm{Na}:[\mathrm{Ne}]3s^1$. Losing its single valence electron produces $\mathrm{Na^+}:[\mathrm{Ne}]$. Chlorine has $\mathrm{Cl}:[\mathrm{Ne}]3s^2 3p^5$ and tends to gain one electron, producing $\mathrm{Cl^-}:[\mathrm{Ne}]3s^2 3p^6=[\mathrm{Ar}]$. The electrostatic attraction between $\mathrm{Na^+}$ and $\mathrm{Cl^-}$ contributes to ionic sodium chloride.

Atoms can also share electrons through covalent bonds. Carbon has four valence electrons and commonly forms four covalent bonds. Oxygen has six valence electrons and commonly forms two bonds or gains two electrons. Valence-electron arrangements help predict formulas, bonding patterns, molecular geometry, and polarity.

Reactivity follows periodic properties. Alkali-metal reactivity generally increases down the group because the single valence electron is farther from the nucleus and easier to remove. Halogen reactivity generally decreases down the group because increasing size and shielding weaken the attraction for an added electron.

Consider magnesium and chlorine. Magnesium has $Z=12$, configuration $[\mathrm{Ne}]3s^2$, and two valence electrons. Chlorine has $Z=17$, configuration $[\mathrm{Ne}]3s^2 3p^5$, and seven valence electrons. Because both are in period $3$, their valence electrons occupy the same principal energy level. Chlorine has more protons and a larger effective nuclear charge, so it has a smaller radius, higher first ionization energy, and stronger attraction for electrons than magnesium. Magnesium tends to form $\mathrm{Mg^{2+}}$, while chlorine tends to form $\mathrm{Cl^-}$, helping explain the formation of ionic $\mathrm{MgCl_2}$.

Takeaway: Electron configuration explains whether an atom is likely to lose, gain, or share electrons, while periodic trends explain how strongly it does so.

A Strategy for Solving Atomic-Structure Problems

Use the following sequence to solve quantitative and comparative problems:

1. Identify the element from its atomic number.

2. Determine protons, neutrons, and electrons. For an ion, use $q=\text{protons}-\text{electrons}$.

3. Write the electron configuration and check that its superscripts sum to the electron count.

4. Locate the element’s group, period, and block on the periodic table.

5. Select the relevant trend and explain it using nuclear charge, shielding, radius, energy levels, or valence electrons.

6. Check units and significant figures. Isotopic masses are commonly expressed in $\mathrm{u}$, ionization energies in $\mathrm{kJ\,mol^{-1}}$, and abundances as percentages or decimal fractions.

For a comparison, do not merely state that one property is larger. Connect the observation to a cause. For example, if two elements are in the same period, their valence electrons occupy the same principal energy level. The element with more protons generally has a larger effective nuclear charge, which tends to produce a smaller atomic radius and higher first ionization energy.

For isotope calculations, convert percentages to fractions, multiply each isotope mass by its fractional abundance, and add the contributions:

For ion calculations, determine the proton count from the element, calculate neutrons from $A-Z$, and use the charge to determine electrons. Then write the configuration for that electron count rather than for the neutral atom.

Final checklist:

• Did you distinguish atomic number from mass number?

• Did you account for ion charge when counting electrons?

• Do configuration superscripts add correctly?

• Did you identify the valence electrons?

• Did you explain a trend using effective nuclear charge and shielding?

• Did you include appropriate units and precision?

Overall takeaway: Atomic structure is a connected system: proton number identifies the element, electron configuration determines valence behavior, and nuclear attraction and shielding produce the periodic trends used to predict chemical behavior.

• periodic trend