Question

Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

Hint:

Quantization effects become observable only when the action involved is comparable to Planck's constant \(h\). For macroscopic objects such as planets, \[ L \gg \frac{h}{2\pi}, \] so quantum effects are practically unobservable and classical mechanics works extremely well.

Answer 1

Rutherford Scattering Graph Concept: In Rutherford's alpha-particle scattering experiment, a beam of alpha particles is directed towards a thin metallic foil. Most alpha particles pass through the foil without any significant deflection, while a very small fraction undergoes large-angle scattering. The number of scattered particles decreases rapidly as the scattering angle increases. Required Graph:

The graph shows a very large number of particles scattered through small angles and a very small number scattered through large angles. Conclusion 1: Most of the atom is empty space. Since the vast majority of alpha particles pass through the foil without any deflection, most of the volume of the atom contains no concentrated mass or charge. Therefore, \[ \boxed{\text{Most of the atom is empty space.}} \] Conclusion 2: Positive charge and mass are concentrated in a very small central region. A few alpha particles are scattered through very large angles and some even rebound. Such large deflections are possible only if the positive charge and most of the mass are concentrated in a tiny central region. Therefore, \[ \boxed{\text{The atom contains a small, dense, positively charged nucleus.}} \]