Question

Explain why, at room temperature, fluorine and chlorine are gases, bromine is a liquid, and iodine is a solid.

Short answer

Weak dispersion forces which grow down the group.

Step-by-step solution

Define Dispersion forces

The London or dispersion force is a transient attractive force that occurs when the electrons in two vicinal atoms acquire positions that make the atoms form temporary dipoles.

Step 2: At room temperature, fluorine and chlorine are gases, bromine is a liquid, and iodine is a solid:

The reason for this effect is that the weak dispersion forces which act among the molecules grow down the group.

Forces among molecules are much weaker then the forces.
Another reason is that the higher the mass of atoms, the less volatile are its gas vapors.

In other words, the heavier the molecules are, it is harder for them to escaping the liquid (at certain temperature).