Recall the general trends down a group in the periodic table:

• Atomic radius generally increases down a group because new shells are added.
• Electronegativity generally decreases down a group because the valence electrons are farther from the nucleus and shielding increases.
• Electron gain enthalpy generally becomes less negative down a group, so its tendency to accept electrons decreases.

We need the property that decreases down a group and the property that increases down a group, respectively.

So we are looking for:

$\text{decreases} \; \to \; \text{Electronegativity}$ $\text{increases} \; \to \; \text{Atomic Radius}$

Check each option:

• A: Atomic Radius and Electronegativity

  • Atomic radius does not decrease; it increases.
  • Electronegativity does not increase; it decreases.
  • Incorrect.

• B: Electron Gain Enthalpy and Electronegativity

  • Electron gain enthalpy generally decreases in magnitude down a group, but electronegativity does not increase.
  • Incorrect.

• C: Electronegativity and Atomic Radius

  • Electronegativity decreases down a group.
  • Atomic radius increases down a group.
  • Correct.

• D: Electronegativity and Electron Gain Enthalpy

  • Electronegativity decreases, but electron gain enthalpy does not generally increase down a group.
  • Incorrect.

Therefore, the correct answer is:

$\boxed{\text{C: Electronegativity and Atomic Radius}}$