Periodic Trends in Physical Properties

Effective nuclear charge does the driving. A valence electron never feels the full pull of all $Z$ protons — inner-shell electrons sit between it and the nucleus and cancel part of that pull. The net charge actually felt is

where: $Z$ is the atomic number (total protons), $\sigma$ is the shielding constant contributed by inner, filled shells, and $Z_{eff}$ is the effective nuclear charge felt by an outer electron. Across a period, $Z$ climbs by one unit at a time while electrons keep filling the same outer shell, so shielding barely changes and $Z_{eff}$ rises steadily. Down a group, a brand-new outer shell opens up each time, so the extra inner shells shield far more effectively — $Z_{eff}$ stays roughly similar even as $Z$ climbs, but the outer electron now sits in a shell of larger radius $n$.

Atomic and ionic radius follow directly. Across a period, rising $Z_{eff}$ pulls the same-shell electron cloud inward, so atomic radius shrinks left to right. Down a group, the new outer shell dominates over the modest rise in $Z_{eff}$, so radius grows. Ions obey the same logic adjusted for charge: a cation is smaller than its parent atom (one fewer electron, same nuclear pull), an anion is larger (one more electron, more electron-electron repulsion), and within an isoelectronic series — same electron count, different $Z$ — radius shrinks as $Z$ rises, because every electron now feels a bigger $Z_{eff}$.

Ionisation enthalpy, electron gain enthalpy and electronegativity all track $Z_{eff}$ in the same direction. Ionisation enthalpy (energy to remove the outermost electron, in $\text{kJ mol}^{-1}$) generally rises across a period and falls down a group, because a tightly held, close-in electron is harder to pull away. Electron gain enthalpy (energy change on adding an electron to a neutral atom) generally becomes more negative across a period and less negative down a group, for the same reason — a higher $Z_{eff}$ welcomes the extra electron more strongly. Electronegativity, the pull an atom in a molecule exerts on a shared bonding pair, rises across a period and falls down a group. All four properties are really one story told four ways.

Question: Arrange Na, Mg, Al, Si (period 3) in order of increasing first ionisation enthalpy, explaining any exception to the general period trend, and state what this predicts about their atomic radii.

Step 1. Write the outer configurations: Na is $3s^1$, Mg is $3s^2$, Al is $3s^2 3p^1$, Si is $3s^2 3p^2$.

Step 2. Apply the plain period trend first. $Z_{eff}$ rises steadily from Na to Si, so the naive prediction — ignore subshell stability for a moment — is a smooth increase: Na less than Mg less than Al less than Si.

Step 3. Check for the stability exception. Mg has a completely filled $3s^2$ subshell, which is extra stable and resists losing an electron more than the naive $Z_{eff}$ trend suggests. Al's outermost electron instead comes from the higher-energy, less-penetrating $3p^1$ orbital, which is comparatively easy to remove even though Al has a higher $Z_{eff}$ than Mg. Net effect: Al's first ionisation enthalpy drops below Mg's.

Step 4. State the corrected order and the radius consequence. The corrected ionisation-enthalpy order is Na < Al < Mg < Si. Since ionisation enthalpy broadly tracks the same rising $Z_{eff}$ that shrinks atomic radius, the radius order across the same four atoms runs the opposite way, largest to smallest: Na > Mg > Al > Si (radius has no subshell-stability exception the way ionisation enthalpy does, since it depends only on where the outermost shell sits, not on which subshell the last electron left).

Answer: ionisation enthalpy order Na < Al < Mg < Si, with radius shrinking steadily Na > Mg > Al > Si.

• Assuming atomic radius drops on every single step across a period with no exception — the big drop from a noble gas to the next period's alkali metal is a jump between periods, not part of the same monotonic run.
• Mixing up ionisation enthalpy (removing an electron, always needs energy, always positive) with electron gain enthalpy (adding an electron, often releases energy, often negative) — they are opposite-direction processes with opposite typical signs.
• Forgetting the half-filled and fully-filled subshell exceptions (Group 2 above Group 13, Group 15 above Group 16 in ionisation enthalpy) and predicting a perfectly smooth period-wide increase.
• Treating electronegativity as a fixed, isolated-atom number like ionisation enthalpy — it is a relative, scale-dependent measure of pull on a shared bonding pair within a molecule, not a standalone atomic property.

Ask the tutor: want to practice ranking a fresh set of atoms or ions by radius, ionisation enthalpy, or electronegativity, or walk through another isoelectronic-series example step by step?