The distance between the a-particle and target nucleus in an `alpha`-scattering experiment is equal to distance of closest approach, when the scattering angle is

Options

A. `pi //2`
B. `pi`
C. `pi //4`
D. `pi //3`

Answer

To solve the problem, we need to understand the concept of the distance of closest approach in an alpha scattering experiment. The distance of closest approach is the minimum distance between the alpha particle and the target nucleus during the scattering process.

### Step-by-Step Solution:

1. **Understanding the Concept**:
- In an alpha scattering experiment, an alpha particle approaches a target nucleus and experiences a repulsive force due to the positive charge of the nucleus. The distance of closest approach is the point at which the kinetic energy of the alpha particle is completely converted into potential energy due to this repulsion.

2. **Identifying the Scattering Angle**:
- The scattering angle is defined as the angle through which the alpha particle is deflected after interacting with the target nucleus. When the alpha particle reaches the distance of closest approach, it momentarily comes to rest before being repelled back.

3. **Condition for Distance of Closest Approach**:
- The distance between the alpha particle and the target nucleus is equal to the distance of closest approach when the alpha particle is directly approaching the nucleus and then reverses its direction. This occurs when the alpha particle is scattered back along the same path it came from.

4. **Calculating the Scattering Angle**:
- When the alpha particle approaches the nucleus and reaches the distance of closest approach, it will scatter back in the opposite direction. This means that the scattering angle is 180 degrees (or π radians) because it has turned around completely.

5. **Conclusion**:
- Therefore, the scattering angle when the distance between the alpha particle and the target nucleus is equal to the distance of closest approach is **π radians** (or 180 degrees).

### Final Answer:
The scattering angle is π radians (or 180 degrees).