Question

Draw the graph showing the variation of number of scattered alpha particles \((N)\) detected with scattering angle \((\theta)\) in Geiger-Marsden experiment. Infer two conclusions from the graph.

Hint:

Remember Rutherford's two most important conclusions:
• Atom is mostly empty space.
• Positive charge and mass are concentrated in a tiny nucleus.

Answer 1

Explanation of the Graph:

• The horizontal axis represents the scattering angle \((\theta)\).
• The vertical axis represents the number of scattered alpha particles \((N)\).
• The graph shows that the number of scattered particles decreases rapidly as the scattering angle increases.
• A very large number of alpha particles are scattered through small angles, while only a few are scattered through large angles.
• Very few alpha particles are scattered through angles close to \(180^\circ\) (back scattering).

Conclusions from the Graph

1. Most of the atom is empty space.
   Since the majority of alpha particles pass through the foil without any significant deflection, they do not encounter any obstruction inside the atom.
2. The positive charge and almost the entire mass of the atom are concentrated in a very small, dense nucleus.
   The small number of alpha particles scattered through large angles or reflected back indicates the presence of a tiny, massive, positively charged nucleus at the centre of the atom.

Key Observation

The probability of scattering decreases sharply with increasing scattering angle, i.e.,

\[ N \propto \frac{1}{\sin^4\left(\frac{\theta}{2}\right)} \]

Thus, large-angle scattering is extremely rare compared to small-angle scattering.