The interaction energy of London forces between two particles is proportional to r\(^x\), where r is the distance between the particles. The value of x is :
Show Hint
Memorize the distance dependence of potential energy for the main types of intermolecular interactions. London dispersion forces, being the weakest and arising from fluctuating dipoles, have a strong distance dependence of 1/r\(^6\), meaning they are very short-range forces.
Step 1: Understanding the Question:
The question asks for the relationship between the interaction energy of London dispersion forces and the distance `r` between the particles. Step 2: Key Formula or Approach:
This is a direct question based on the theory of intermolecular forces. We need to recall the distance dependence of the potential energy for different types of van der Waals forces. Step 3: Detailed Explanation:
Intermolecular forces are categorized into several types. The London dispersion force is a type of van der Waals force that arises from temporary, fluctuating dipoles in nonpolar molecules.
The potential energy (U) of interaction between molecules depends on the distance `r` between them.
- For ion-dipole interaction, U \(\propto\) 1/r\(^2\).
- For dipole-dipole interaction (Keesom forces), U \(\propto\) 1/r\(^3\) for rotating dipoles and U \(\propto\) 1/r\(^6\) for stationary dipoles.
- For dipole-induced dipole interaction (Debye forces), U \(\propto\) 1/r\(^6\).
- For London dispersion forces (induced dipole-induced dipole), the interaction energy is also proportional to 1/r\(^6\).
Therefore, the interaction energy U is proportional to \( \frac{1}{r^6} \), which can be written as \( U \propto r^{-6} \).
The question states the energy is proportional to r\(^x\). Comparing this with our finding, we get x = -6. Step 4: Final Answer:
The value of x is -6. This corresponds to option (D).
