At room temperature `F_2` and `Cl_2` are gases `Br_2` is a liquid and `I_2` is solid. This is because

Options

A. Dipole-induced dipole interaction increases with molecular size
B. Dipole-dipole interactions increases with molecular size
C. Dispersion (London) interaction increases with molecular size
D. Dispersion ( London) interactions decreases with molecular size and polarity increases with molecular size

Answer

To answer the question regarding the states of matter of the halogens (F₂, Cl₂, Br₂, and I₂) at room temperature, we can follow these steps:

### Step 1: Identify the Group
All the given elements (F₂, Cl₂, Br₂, and I₂) belong to Group 17 of the periodic table, which is known as the halogens.

**Hint:** Remember that elements in the same group often exhibit similar chemical properties.

### Step 2: Understand the States of Matter
At room temperature:
- F₂ (Fluorine) and Cl₂ (Chlorine) are gases.
- Br₂ (Bromine) is a liquid.
- I₂ (Iodine) is a solid.

**Hint:** Consider how temperature affects the state of matter based on intermolecular forces.

### Step 3: Analyze Intermolecular Forces
All these halogens are non-polar molecules. The primary intermolecular forces present in non-polar molecules are London dispersion forces (also known as van der Waals forces).

**Hint:** Recall that non-polar molecules do not have dipole-dipole interactions.

### Step 4: Relate Molecular Size to Intermolecular Forces
As we move down the group from F₂ to I₂, the size of the molecules increases. With an increase in molecular size, the strength of the London dispersion forces also increases.

**Hint:** Larger molecules have more electrons, which can lead to stronger temporary dipoles and thus stronger dispersion forces.

### Step 5: Determine the Effect on States of Matter
- F₂ has the smallest size and the weakest London dispersion forces, which is why it is a gas.
- Cl₂ is larger than F₂, has stronger dispersion forces, and is also a gas.
- Br₂ is larger than Cl₂, has even stronger dispersion forces, and is a liquid.
- I₂ has the largest size and the strongest dispersion forces, which makes it a solid.

**Hint:** Think about how stronger intermolecular forces affect the arrangement and movement of particles in different states of matter.

### Conclusion
The reason for the different states of matter at room temperature is due to the increase in London dispersion forces as the molecular size increases down the group. Thus, the correct explanation is that "dispersion (London) interaction increases with molecular size."

**Final Answer:** The correct option is that "dispersion (London) interaction increases with molecular size."