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?

Question

Given below are two statements :
Statement I : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford’s model.
Statement II : An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford’s model.
In the light of the above statements, choose the most appropriate from the options given below.

Answer 1

Step 1: Recall Rutherford's scattering law.
The number of alpha-particles scattered at angle $\theta$ follows $N(\theta) \propto \dfrac{1}{\sin^4(\theta/2)}$.
Step 2: Behaviour at small angles.
For small $\theta$, $\sin(\theta/2)$ is tiny, so $N(\theta)$ becomes very large. Most particles barely deflect.
Step 3: Behaviour at large angles.
As $\theta$ grows, $\sin(\theta/2)$ grows and $N(\theta)$ drops steeply toward zero. Very few particles bounce back.
Step 4: Describe the curve.
So the plot starts extremely high at small angles and falls off sharply, never turning back up.
Step 5: Match the shape to a graph.
This steeply decreasing curve is the one shown as Graph (4).
Step 6: State the answer.
The correct plot is option D.
\[ \boxed{\text{Graph (4)}} \]

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

The Correct Option is D

Solution and Explanation

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