The intermolecular interaction for which interaction energy that is inversely proportional to the cube of distance between the molecule is

Options

A. Ion-ion interaction
B. Ion-dipole interaction
C. London forces
D. Dipole-dipole forces

Answer

To determine the intermolecular interaction for which the interaction energy is inversely proportional to the cube of the distance between the molecules, we can analyze the types of intermolecular forces and their corresponding mathematical representations.

### Step-by-Step Solution:

1. **Understanding Intermolecular Forces**:
Intermolecular forces include various types such as ion-ion, ion-dipole, dipole-dipole, and London dispersion forces. Each of these forces has a specific relationship between interaction energy and distance.

2. **Mathematical Representation**:
The interaction energy (U) between two molecules can often be expressed as:
\[ U \propto \frac{1}{r^n} \]
where \( r \) is the distance between the molecules and \( n \) is a constant that varies depending on the type of interaction.

3. **Identifying the Relevant Interaction**:
- **Ion-Ion Interaction**: Typically, this interaction is proportional to \( \frac{1}{r} \) (Coulomb's law).
- **Ion-Dipole Interaction**: This interaction is also proportional to \( \frac{1}{r^2} \).
- **Dipole-Dipole Interaction**: This interaction is proportional to \( \frac{1}{r^3} \).
- **London Dispersion Forces**: These are also proportional to \( \frac{1}{r^6} \).

4. **Conclusion**:
The intermolecular interaction for which the interaction energy is inversely proportional to the cube of the distance between the molecules is the **dipole-dipole interaction**. This means that as the distance between two polar molecules increases, the strength of the dipole-dipole interaction decreases with the cube of that distance.

### Final Answer:
The intermolecular interaction for which the interaction energy is inversely proportional to the cube of the distance between the molecules is **dipole-dipole interaction**.

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