Periodic Trends

A periodic trend is a predictable change in an atomic property as you move across a period (left to right, same energy level) or down a group (top to bottom, same valence configuration). The four trends on this sheet, atomic radius, ionization energy, electronegativity, and metallic character, all trace back to just two competing forces: how hard the nucleus pulls on the outer electrons, and how much the inner electrons block that pull. Once you can predict the direction of the pull, you can predict every trend on this sheet without memorizing four separate rules.

Effective nuclear charge (Zeff) is the net positive pull an outer (valence) electron actually feels, after the inner (core) electrons cancel out part of the nucleus's full charge. It is estimated as: Zeff ≈ Z − S where Z is the number of protons and S is the shielding constant, roughly the number of core electrons sitting between the nucleus and the valence electron. Core electrons repel outer electrons and "screen" them from the full nuclear charge; this is electron shielding (also called the screening effect).

Atomic radius is roughly half the distance between the nuclei of two bonded identical atoms. Trend: decreases across a period, increases down a group. Across a period, rising Zeff pulls the same-shell electrons in tighter, so the atom shrinks even though it is gaining electrons. Down a group, each row adds a new occupied shell, which outweighs the extra nuclear pull, so the atom gets bigger. The largest atoms sit in the lower-left of the table (cesium, francium). The smallest reactive atoms sit in the upper-right (fluorine). Noble gases are measured differently, so helium is technically the smallest atom of all, but it is set aside from the reactive trend.

Ionic radius follows related but distinct rules: - A cation (positive ion, e.g. Na⁺) is always smaller than its parent atom. It has lost an entire outer shell of electrons and often lost the electron-electron repulsion that was stretching the atom out. - An anion (negative ion, e.g. Cl⁻) is always larger than its parent atom. Added electrons increase electron-electron repulsion in the same shell without adding protons to compensate. - For an isoelectronic series (same electron count, different Z), radius shrinks as Z increases, e.g. O²⁻ > F⁻ > Na⁺ > Mg²⁺ > Al³⁺, all have 10 electrons, but more protons means a tighter pull.

First ionization energy (IE₁) is the energy required to remove the outermost electron from a neutral gaseous atom: X(g) → X⁺(g) + e⁻. Trend: increases across a period, decreases down a group, the mirror image of atomic radius. Higher Zeff (across a period) means the outer electron is held more tightly and takes more energy to remove. A larger atomic radius (down a group) means the outer electron is farther from the nucleus, more shielded, and easier to pull off.

Successive ionization energies (IE₂, IE₃, ...) always increase. Removing an electron from an already-positive ion is harder, since there is less electron-electron repulsion and more net positive pull per remaining electron. Watch for a huge jump right after the last valence electron is removed, that jump signals you have reached the noble-gas core and started breaking into an inner shell.

Electronegativity is an atom's relative pull on shared electrons in a covalent bond, measured on the Pauling scale (no units). Trend: increases across a period, decreases down a group, same logic as ionization energy: high Zeff and small radius mean an atom pulls bonding electrons toward itself harder. Fluorine is the most electronegative element on the table (3.98). Noble gases are normally excluded, they do not typically form bonds, so the trend is usually described as running toward the top-right corner minus group 18.

Metallic character describes how easily an element loses electrons to form a cation and how strongly it shows classic metal behavior (shiny, malleable, conducts electricity, forms basic oxides). Trend: increases down a group, decreases across a period (left to right), the exact opposite direction of ionization energy and electronegativity, because losing an electron is easiest when the atom is large and holds its outer electron loosely (low Zeff felt by the valence electron, big radius). The most metallic elements sit in the lower-left of the table (cesium, francium); the least metallic (most nonmetallic) sit in the upper-right (fluorine, oxygen).

Memory aid: picture an arrow pointing from francium (bottom-left) toward fluorine (top-right). Atomic radius and metallic character point the *opposite* way, they are biggest at francium's corner. Ionization energy and electronegativity point *with* the arrow, they are highest at fluorine's corner (excluding noble gases, which have the highest ionization energy in their period but are not assigned an electronegativity).

1. Rank Mg, Al, and Na by atomic radius, largest to smallest. (All are period 3, so compare Zeff: Na has the lowest Zeff on its valence electron, so Na > Mg > Al.) 2. Explain why the first ionization energy of oxygen is lower than nitrogen's, even though oxygen has one more proton. (Removing an electron from O's paired 2p orbital relieves electron-electron repulsion, while N's 2p³ is half-filled and extra stable, making N harder to ionize than the trend alone would predict.) 3. Without looking at a chart, predict which has greater metallic character: calcium or gallium, and justify it using Zeff and shielding. (Calcium is farther left in period 4 with a lower Zeff on its valence electrons and a larger radius, so it loses electrons more easily. Calcium has greater metallic character than gallium.)

Using periodic-trends-reference-values.csv: 4. Rank all 8 elements by atomic radius, largest to smallest. 5. Which element in the file has the highest first ionization energy? Which has the lowest? 6. Rank Li, Na, and K (the group 1 elements in the file) by electronegativity, lowest to highest, and state whether this matches the "electronegativity decreases down a group" trend. 7. Looking only at the period-2 elements in the file (Li, Be, B, N, O) and their first-ionization-energy values, in order, identify BOTH pairs of consecutive elements where the ionization energy goes DOWN instead of up, and name the extra-stable subshell that causes each dip.