In the geiger -marsden scattering experiment, in case of head- on collision the impact parameter should be

Options

A. maximum
B. minimum
C. infinite
D. zero

Explanation

To determine the impact parameter in a head-on collision during the Geiger-Marsden scattering experiment, we can follow these steps:

### Step 1: Understand the Concept of Impact Parameter
The impact parameter (B) is defined as the perpendicular distance from the center of the nucleus to the path of the incoming particle (in this case, an alpha particle).

### Step 2: Identify the Condition for Head-On Collision
In a head-on collision, the alpha particle travels directly towards the center of the nucleus. This means that the distance from the center of the nucleus to the path of the alpha particle is zero.

### Step 3: Analyze the Equation for Impact Parameter
The equation for the impact parameter (B) is given by:
\[ B = \frac{Z e^2 \cot(\theta/2)}{4 \pi \epsilon_0 e} \]
where:
- \( Z \) is the atomic number of the nucleus,
- \( e \) is the charge of the alpha particle,
- \( \epsilon_0 \) is the permittivity of free space,
- \( \theta \) is the scattering angle.

### Step 4: Substitute the Scattering Angle for Head-On Collision
For a head-on collision, the scattering angle \( \theta \) is equal to 180 degrees. Thus, we can substitute \( \theta = 180^\circ \) into the equation.

### Step 5: Calculate the Impact Parameter
Substituting \( \theta = 180^\circ \) into the equation:
\[ B = \frac{Z e^2 \cot(180^\circ/2)}{4 \pi \epsilon_0 e} \]
This simplifies to:
\[ B = \frac{Z e^2 \cot(90^\circ)}{4 \pi \epsilon_0 e} \]

### Step 6: Evaluate the Cotangent Function
We know that:
\[ \cot(90^\circ) = 0 \]
Therefore:
\[ B = \frac{Z e^2 \cdot 0}{4 \pi \epsilon_0 e} = 0 \]

### Conclusion
The impact parameter \( B \) for a head-on collision is zero.

### Final Answer
Thus, the impact parameter in the case of a head-on collision is **zero**.

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