In Rutherford scattering experiment for scattering angle of `180^(@)`, what be the value of impact parameter?

Options

A. 0
B. `oo`
C. 1
D. Data is insufficient

Explanation

To solve the question regarding the impact parameter in the Rutherford scattering experiment for a scattering angle of \(180^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**:
The impact parameter \(d\) is related to the scattering angle \(\theta\) by the formula:
\[ d = k \cdot \cot\left(\frac{\theta}{2}\right) \]
where \(k\) is a proportionality constant.

2. **Substitute the Given Angle**:
We are given that the scattering angle \(\theta = 180^\circ\). We will substitute this value into the formula:
\[ d = k \cdot \cot\left(\frac{180^\circ}{2}\right) \]

3. **Calculate the Angle**:
Calculate \(\frac{180^\circ}{2}\):
\[ \frac{180^\circ}{2} = 90^\circ \]

4. **Evaluate the Cotangent**:
Now, we find \(\cot(90^\circ)\):
\[ \cot(90^\circ) = 0 \]

5. **Final Calculation**:
Substitute \(\cot(90^\circ)\) back into the equation for \(d\):
\[ d = k \cdot 0 = 0 \]

6. **Conclusion**:
Therefore, the value of the impact parameter \(d\) for a scattering angle of \(180^\circ\) is:
\[ d = 0 \]

### Final Answer:
The impact parameter is \(0\).

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