Number of the `alpha`- particle deflected in Rutherford's `alpha` -scattering experiment varies with the angle of deflection. Then the graph between the two is best represented by.

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Answer

To solve the problem regarding the relationship between the number of alpha particles deflected and the angle of deflection in Rutherford's alpha-scattering experiment, we can follow these steps:

### Step 1: Understand the Experiment
Rutherford's alpha-scattering experiment involved firing alpha particles at a thin gold foil. Most alpha particles passed straight through the foil, while a small fraction were deflected at various angles.

### Step 2: Analyze the Deflection
The key observations from the experiment are:
- Most of the alpha particles (about 99%) pass through the foil without any deflection (0 degrees).
- A small number of alpha particles are deflected at small angles.
- An even smaller number are deflected at larger angles, with very few being deflected back (180 degrees).

### Step 3: Relationship Between Deflection and Angle
The number of alpha particles deflected at a specific angle decreases as the angle increases. This is because:
- The likelihood of deflection is higher at smaller angles due to the greater cross-sectional area of the nucleus that the alpha particles can interact with.
- As the angle increases, the effective area for interaction decreases, leading to fewer deflections.

### Step 4: Graphical Representation
Based on the above analysis, if we were to plot a graph with the angle of deflection (θ) on the x-axis and the number of deflected alpha particles on the y-axis, we would expect:
- A high number of deflections at small angles (close to 0 degrees).
- A rapid decrease in the number of deflections as the angle increases.
- The graph would likely show a curve that starts high and drops off steeply, resembling an exponential decay or a hyperbolic shape.

### Conclusion
The graph that best represents the relationship between the number of alpha particles deflected and the angle of deflection is a decreasing curve, starting high at small angles and dropping off as the angle increases.