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:

Rutherford scattering key idea:

Most particles undeflected → empty space
Few large-angle deflections → tiny dense nucleus

Answer 1

Scattering of Alpha Particles: Graph and Conclusions
The scattering of alpha particles by a thin foil (as in Rutherford’s experiment) can be represented by a plot of number of scattered particles versus scattering angle (\( \theta \)). 
Graph:

In the graph: - The y-axis represents the number of alpha particles scattered. - The x-axis represents the scattering angle (\( \theta \)). - Most particles are scattered at very small angles, while very few are scattered at large angles. 
Two Important Conclusions:
1. Most alpha particles pass through undeflected: This indicates that the atom is mostly empty space, allowing most alpha particles to go straight through the foil without any deflection.
2. Some particles are deflected at large angles: A small number of alpha particles experience large-angle deflections, which implies the presence of a very small, dense, positively charged nucleus at the center of the atom that repels the alpha particles.
Summary:
The plot confirms Rutherford’s nuclear model of the atom: atoms consist of a tiny, dense, positively charged nucleus surrounded by electrons, with most of the atom being empty space. The scattering distribution is key evidence for the nuclear structure of the atom.
 

Answer 2

Another useful way to draw conclusions from this plot is by comparing what it actually shows against what the older plum-pudding model of the atom, in which positive charge and mass were thought to be spread out evenly through the whole atom, would have predicted.

What the plum-pudding model predicted:
If positive charge were spread thinly and evenly throughout the atom's volume, an alpha particle passing through would feel only a weak, gradually varying force at any point, never a strong, localized repulsion. Under this picture, essentially every alpha particle should undergo only small deflections, and large-angle scattering events should be so vanishingly rare that they are effectively never seen.

What the plot actually shows:
The number of scattered particles is very high at small angles near \( \theta = 0^\circ \), which does agree with the plum-pudding prediction of mostly gentle deflection. But the curve does not fall to exactly zero at large angles, a small but clearly measurable number of alpha particles are scattered through large angles, and a very small number are scattered back at angles approaching \( 180^\circ \), essentially bouncing straight back.

Where the two disagree, and what it implies:
The presence of these rare, large-angle events directly contradicts the uniformly-spread-charge picture: no combination of many weak, gradual deflections from a spread-out charge distribution can add up to send an alpha particle almost straight back. Such a sharp reversal needs a single strong, close-range repulsive encounter.

Conclusion 1: the atom is mostly empty space.
The very large number of particles passing through with negligible deflection shows that, contrary to a uniformly filled atom, most of an atom's volume contains nothing capable of significantly deflecting a fast alpha particle.

Conclusion 2: an atom has a small, dense, positively charged nucleus at its centre.
The rare large-angle and near-back-scattered particles can only be explained if the positive charge is not spread out but is instead concentrated in a very small volume, dense and charged enough to repel an alpha particle strongly enough to reverse its path on a close encounter, ruling out the plum-pudding picture and supporting a small central nucleus.