Predicting Trends: Sodium vs Magnesium

Given

• Sodium: Z = 11, Period 3, Group 1 (valence shell n = 3)

• Magnesium: Z = 12, Period 3, Group 2 (valence shell n = 3)

• Both valence electrons occupy the same n = 3 shell

Find

Which of Na vs Mg has the larger atomic radius and the lower first ionization energy, with explanation.

Principle

Across a period, each step right adds a proton but the added electrons go into the same shell, so inner electrons shield almost as before and the effective nuclear charge felt by the valence shell rises. Stronger pull shrinks the atom and holds the outermost electron more tightly, so atomic radius falls and ionization energy climbs.

Formula

Solution

1. Locate both in Period 3: Na is Z = 11, Mg is Z = 12, and both have valence electrons in the n = 3 shell.

2. Across Period 3 the nuclear charge grows from 11 to 12 while inner-shell shielding stays nearly the same, so Mg's valence electrons feel a higher effective nuclear charge than Na's.

3. Higher Z_eff pulls the n = 3 shell closer in Mg, so magnesium is smaller: Na has the larger atomic radius.

4. Because Na's valence electron is farther out and less tightly held, it is easier to remove: sodium has the lower first ionization energy.

Unit check

Trends are comparisons, not calculations with units: atomic radius is measured in picometers and ionization energy in kJ/mol, but the prediction asks only for the direction of change, which the Z_eff argument provides without any numbers.

What this means physically

This is the periodic table in miniature: moving one step right across Period 3 makes the atom smaller and harder to ionize. The same effective-nuclear-charge logic predicts every across-a-period trend, so mastering this one comparison unlocks dozens of predictions.