Statement-1: Impact parameter for scattering of `alpha` particles by `180^(@)` is zero.
Statement-2 : Zero impact parameter means `alpha` particle tends to hit the centre of the nucleus

Options

A. Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation of Statement-1.
B. Statement-1 is true, Statement-2 is true, but Statement-2 is not a correct explanation of Statement-1.
C. Statement-1 is true, but Statement-2 is false
D. Statement-1 is false, but Statement-2 is true.

Explanation

To solve the given question, we need to analyze both statements about the impact parameter and the scattering of alpha particles.

### Step-by-Step Solution:

1. **Understanding Impact Parameter**:
- The impact parameter (denoted as \( B \)) is defined as the perpendicular distance from the center of the nucleus to the trajectory of the incoming alpha particle. It is a measure of how close the alpha particle comes to the nucleus before being deflected.

**Hint**: Recall that the impact parameter is crucial in determining the scattering angle of particles in a collision.

2. **Analyzing Statement 1**:
- Statement 1 claims that the impact parameter for scattering of alpha particles by \( 180^\circ \) is zero.
- When an alpha particle is scattered at \( 180^\circ \), it means that it has been deflected back in the direction from which it came. This scenario occurs when the alpha particle comes directly towards the nucleus and is repelled back, indicating that it must have passed very close to or directly through the center of the nucleus.

**Hint**: Consider the relationship between the scattering angle and the impact parameter. What does a \( 180^\circ \) scattering angle imply about the trajectory?

3. **Calculating Impact Parameter for \( 180^\circ \)**:
- The formula for the impact parameter \( B \) can be expressed in terms of the scattering angle \( \theta \) as:
\[ B = \frac{ze^2 \cot(\theta/2)}{4\pi \epsilon_0 E} \]
- If we set \( \theta = 180^\circ \), then \( \cot(90^\circ) = 0 \). Thus, substituting this into the formula gives:
\[ B = 0 \]
- This confirms that the impact parameter is indeed zero when the scattering angle is \( 180^\circ \).

**Hint**: Remember that trigonometric functions can help simplify calculations, especially in determining angles.

4. **Analyzing Statement 2**:
- Statement 2 states that a zero impact parameter means the alpha particle tends to hit the center of the nucleus.
- Since we established that an impact parameter of zero indicates that the particle is on a direct collision course with the nucleus, it follows that the alpha particle would indeed hit the center of the nucleus.

**Hint**: Think about what it means for a particle to have a zero distance from a target in terms of collision dynamics.

5. **Conclusion**:
- Both statements are true. Statement 1 is correct because a scattering angle of \( 180^\circ \) corresponds to an impact parameter of zero. Statement 2 is also true because a zero impact parameter implies that the alpha particle is hitting the nucleus at its center.
- Therefore, the correct answer is that both statements are true, and Statement 2 correctly explains Statement 1.

### Final Answer:
Both Statement 1 and Statement 2 are true, and Statement 2 is the correct explanation of Statement 1.