Key result of Rutherford scattering

In Rutherford's gold foil experiment, the number of scattered $\alpha$-particles at scattering angle $\theta$ follows the Rutherford scattering formula:

$\frac{dN}{d\Omega} \propto \frac{1}{\sin^4(\theta/2)}$

This means:

• For small $\theta$, $\sin(\theta/2)$ is very small, so $\frac{1}{\sin^4(\theta/2)}$ becomes very large.
• For large $\theta$ (toward $180^\circ$), the value becomes much smaller.

So the number of detected $\alpha$-particles is:

• maximum at very small scattering angles, and
• decreases rapidly as $\theta$ increases.

Shape of the graph

Therefore, the correct graph of $Y$ (number of scattered $\alpha$-particles detected) versus $\theta$ must show:

• a very high value near $\theta = 0$,
• then a sharp fall with increasing angle,
• and very few particles at large angles.

Matching with the options

Among the given schematic plots, the one representing a steeply decreasing curve with increasing $\theta$ is Option C.

Conclusion

Hence, the graph depicting Rutherford scattering is:

$\boxed{\text{C}}$

Comparison with stored answer

Stored correct answer = C.

My derived answer also = C. So they agree.