In the Geiger-Marsden experiment, the number of scattered \(\alpha\)-particles \(N(\theta)\) is plotted as a function of scattering angle \(\theta\). Which of the following options represents the correct plot?
Show Hint
Rutherford scattering predicts that most alpha particles suffer very small deflections and only a few are scattered through large angles.
• Rutherford scattering law states:
\[
N(\theta)\propto \frac{1}{\sin^4(\theta/2)}
\]
• Most \(\alpha\)-particles are scattered through small angles.
• Very few particles are scattered through large angles.
Step 1: Examine the scattering formula.
\[
N(\theta)\propto \frac{1}{\sin^4(\theta/2)}
\]
As \(\theta\) increases, \(\sin(\theta/2)\) increases.
Therefore \(N(\theta)\) decreases rapidly.
Step 2: Analyze the nature of the graph.
At very small angles,
\[
N(\theta)
\]
is extremely large.
At larger angles,
\[
N(\theta)
\]
falls sharply toward zero.
This corresponds to Graph (4).
\[
\boxed{\text{Option (D)}}
\]
