According to C.E van der Waal, the interatomic potential varies with the average interatomic distance (R) as

Options

A. `R^(-1)`
B. `R^(-2)`
C. `R^(-4)`
D. `R^(-6)`

Answer

To solve the question regarding how the interatomic potential varies with the average interatomic distance \( r \) according to C.E. van der Waals, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Interatomic Potential**:
The interatomic potential \( V \) describes the energy associated with the interactions between atoms as a function of their distance apart.

2. **Known Relationship**:
According to van der Waals theory, the interatomic potential \( V \) is inversely proportional to the sixth power of the average interatomic distance \( r \). This can be expressed mathematically as:
\[ V \propto -\frac{1}{r^6} \]

3. **Rearranging the Relationship**:
Since we are interested in how \( V \) varies with \( r \), we can rewrite the proportionality:
\[ V \propto r^{-6} \]
This indicates that the interatomic potential \( V \) is directly proportional to \( r \) raised to the power of \(-6\).

4. **Selecting the Correct Option**:
From the options provided:
- Option 1: \( r^{-1} \)
- Option 2: \( r^{-2} \)
- Option 3: \( r^{-4} \)
- Option 4: \( r^{-6} \)

We can see that the correct relationship we derived, \( V \propto r^{-6} \), matches with **Option 4**.

5. **Conclusion**:
Therefore, the interatomic potential varies with the average interatomic distance \( r \) as:
\[ V \propto r^{-6} \]
Hence, the correct answer is **Option 4: \( r^{-6} \)**.