The graph of the total number of `alpha`-particles scattered at different angles in a given interval of time for `alpha`- particles scattering in the geiger- marsden experiment is given by

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the graph of the total number of alpha particles scattered at different angles in the Geiger-Marsden experiment, we can follow these steps:

### Step 1: Understand the Geiger-Marsden Experiment
The Geiger-Marsden experiment, also known as the Rutherford gold foil experiment, was designed to probe the structure of the atom. In this experiment, alpha particles were directed at a thin foil of gold, and the scattering of these particles was observed.

### Step 2: Identify the Variables
In the context of the question:
- The x-axis represents the scattering angle (θ).
- The y-axis represents the total number of alpha particles scattered.

### Step 3: Analyze the Scattering Pattern
From the experiment, we know that:
- At small angles (close to 0°), a large number of alpha particles are scattered.
- As the angle increases, the number of scattered alpha particles decreases initially.
- At larger angles, there is a small increase in the number of particles scattered due to a few particles scattering at larger angles.

### Step 4: Graph Characteristics
Based on the above analysis, the graph will show:
- A decrease in the number of scattered particles for small angles.
- A minimum point followed by an increase in the number of scattered particles at larger angles.

### Step 5: Choose the Correct Graph
Among the given options, we need to find a graph that reflects this behavior:
- The correct graph will start high at small angles, decrease to a minimum, and then increase again.

### Conclusion
The graph that best represents the scattering of alpha particles in the Geiger-Marsden experiment is the one that shows a decrease followed by an increase in the number of scattered particles as the scattering angle increases. Therefore, the correct option is **Option A**.

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