Periodic trends get taught as a set of arrows to memorize, but every single trend traces back to the same underlying cause, and a free response question almost always wants that cause explained, not just the direction stated.
The real explanation: effective nuclear charge
Effective nuclear charge is the net positive pull an outer electron actually feels, after accounting for the shielding effect of inner electrons. Moving across a period, protons increase but shielding from inner electrons stays roughly constant, so effective nuclear charge increases and pulls electrons in tighter. Moving down a group, an entirely new electron shell is added, which is farther from the nucleus and more shielded, outweighing the increase in protons.
Atomic radius
Atomic radius decreases across a period, since increasing effective nuclear charge pulls the existing electrons in closer. It increases down a group, since each new row adds an entire additional electron shell.
Ionization energy
Ionization energy, the energy needed to remove an electron, increases across a period, since electrons are held more tightly as effective nuclear charge increases. It decreases down a group, since outer electrons are farther from the nucleus and more shielded, making them easier to remove.
Electronegativity
Electronegativity, an atom's pull on shared electrons in a bond, follows the same pattern as ionization energy: increasing across a period, decreasing down a group. Fluorine, in the top right of the periodic table, is the most electronegative element for exactly this reason.
Where students actually lose points here
Stating the trend without explaining why
Writing "electronegativity increases across a period" without connecting it to effective nuclear charge and shielding doesn't earn full credit on a free response question that asks for reasoning.
Mixing up which trends move together
Ionization energy and electronegativity move in the same direction as each other, but atomic radius moves in the opposite direction from both. Confusing these relationships is a common, avoidable error.
Forgetting that shielding, not just proton count, matters
Protons alone don't explain the group trend. It's the added electron shell, and the extra shielding that comes with it, that explains why atoms get bigger and lose electrons more easily going down a group.
One idea, three trends
Once effective nuclear charge and shielding are genuinely understood, atomic radius, ionization energy, and electronegativity stop being three things to memorize and become one idea applied three times.
Common questions
Why does atomic radius decrease across a period?
Because effective nuclear charge increases across a period while shielding stays roughly constant, pulling the existing electrons in closer to the nucleus.
Why is fluorine the most electronegative element?
Fluorine sits in the top right of the periodic table, where effective nuclear charge is high and the atom is small, giving it an especially strong pull on shared electrons in a bond.
Do ionization energy and atomic radius move in the same direction?
No, they move in opposite directions. As atomic radius decreases across a period, ionization energy increases, since electrons held closer to the nucleus are harder to remove.