lecture 12

Study Guide - Smart Notes

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Periodic Trends in the Periodic Table

Atomic Radii

The atomic radius is a measure of the size of an atom, typically the distance from the nucleus to the outermost electron shell. Understanding how atomic radii change across the periodic table is fundamental to predicting chemical behavior.

Atomic radius increases down a group: As you move down a group in the periodic table, each successive element has an additional principal energy level (shell), so the valence electrons are farther from the nucleus. This results in a larger atomic radius.
Atomic radius decreases across a period (left to right): As you move across a period, electrons are added to the same valence shell, but the increasing nuclear charge pulls the electrons closer, resulting in a smaller atomic radius.
Example: Sodium (Na) is larger than chlorine (Cl) in the same period, but potassium (K) is larger than sodium (Na) in the same group.

Effective Nuclear Charge (Zeff)

Effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom. It is less than the actual nuclear charge due to shielding by inner electrons.

Definition: Where is the atomic number (number of protons) and is the number of core (shielding) electrons.
Core electrons efficiently shield outer electrons from the nucleus, while valence electrons do not shield each other effectively.
Periodic trend: Effective nuclear charge increases across a period (left to right) and decreases down a group (top to bottom).
Shielding ability: Electrons in s orbitals shield better than those in p, d, or f orbitals. The trend is s > p > d > f.
Example: In lithium (Li), the 1s electrons shield the 2s electron from the nucleus, so the 2s electron experiences a reduced effective nuclear charge.

Summary of Atomic Radii Trends for Main-Group Elements

Down a group: Atomic size increases due to the addition of principal energy levels, which increases the distance of valence electrons from the nucleus.
Across a period: Atomic size decreases as effective nuclear charge increases, pulling valence electrons closer to the nucleus.
Quantum mechanical prediction: Atoms get larger down a column and smaller across a period.

Conceptual Connection: Effective Nuclear Charge

Which atom’s valence electrons experience the greatest effective nuclear charge?

Among Mg, Al, and S, the valence electrons in S experience the greatest effective nuclear charge, because S is furthest to the right in the period, resulting in a higher Zeff.

Atomic Radii of Transition Elements

Transition metals show different trends compared to main-group elements.

Atomic radii increase down a group, similar to main-group elements.
Across the d-block (period), atomic radii remain relatively constant due to poor shielding by d electrons.
Valence ns2 electrons experience similar effective nuclear charge across the period.
Example: The atomic radius of iron (Fe) is similar to that of cobalt (Co) and nickel (Ni).

Problem Solving: Predicting Atomic Size

To compare atomic sizes, consider both group and period trends.
Down a group: size increases (e.g., C < Si < Ge).
Across a period: size decreases (e.g., Al > Si > P).
When moving diagonally, trends may counteract, making predictions less straightforward.

Magnetic Properties: Paramagnetism and Diamagnetism

Magnetic properties of atoms and ions depend on their electron configurations.

Paramagnetism: Atoms or ions with unpaired electrons are attracted to a magnetic field.
Diamagnetism: Atoms or ions with all electrons paired are slightly repelled by a magnetic field.
Example: Fe3+ is paramagnetic because it has unpaired electrons; Al3+ is diamagnetic because all electrons are paired.

Electronic Configuration and Magnetism

Write the electron configuration for the neutral atom.
For cations, remove electrons from the highest principal quantum number first.
For anions, add electrons to the next available orbital.
Determine if the resulting configuration has unpaired electrons (paramagnetic) or all paired (diamagnetic).
Example: Al3+: [Ne] (diamagnetic); Fe3+: [Ar]3d5 (paramagnetic).

Ionic Radii: Cations and Anions

The size of ions differs from their parent atoms due to changes in electron number and effective nuclear charge.

Cations: Smaller than their parent atoms because loss of electrons increases effective nuclear charge on remaining electrons, pulling them closer.
Anions: Larger than their parent atoms because added electrons increase electron-electron repulsion and decrease effective nuclear charge per electron.
Isoelectronic series: For ions with the same electron configuration, the more positive the charge, the smaller the ion; the more negative, the larger the ion.
Example Table:

Species	Charge	Relative Size
Na+	+1	Smallest
Mg2+	+2	Smaller
O2−	−2	Larger
F−	−1	Largest

Additional info: Table inferred for isoelectronic series (e.g., Na+, Mg2+, O2−, F− all have 10 electrons).

Ionization Energy

Ionization energy (IE) is the minimum energy required to remove an electron from an atom or ion in the gas phase. It is always an endothermic process.

First ionization energy (IE1): Energy to remove the first electron from a neutral atom.
Second ionization energy (IE2): Energy to remove a second electron from a 1+ ion, and so on.
Equation:

Trends:
- IE decreases down a group (valence electrons are farther from the nucleus, less tightly held).
- IE increases across a period (effective nuclear charge increases, electrons held more tightly).
Example: IE1 for Na is lower than for Cl; IE1 for K is lower than for Na.

Summary Table: Periodic Trends

Trend	Down a Group	Across a Period
Atomic Radius	Increases	Decreases
Effective Nuclear Charge (Zeff)	Decreases	Increases
Ionization Energy	Decreases	Increases

Practice and Application

Arrange elements or ions in order of increasing or decreasing size or ionization energy using periodic trends.
Predict magnetic properties based on electron configurations.
Apply the concept of effective nuclear charge to explain trends in atomic and ionic size, as well as ionization energy.