Rutherford scattering — the discovery of the nucleus

What just happened?

You reduced the impact parameter — the alpha particle flew closer to the nucleus, so the Coulomb repulsion was stronger and the scattering angle rose sharply, up to an almost backward deflection.

Rutherford's condition:

— the scattering angle $\theta$ grows as the impact parameter $b$ decreases. $a$ is the approach scale, set by the charges of the nucleus and the particle and by its energy; $b$ — the perpendicular distance of the path from the nucleus.

What does this mean in practice?

Most particles have a large $b$ and fly almost straight through (small angle). Only a few, hitting almost head-on, are deflected at a large angle — because they meet the concentrated, positive charge of the nucleus:

Why did this overturn the "plum pudding" model?

If the mass and charge were smeared across the whole atom, the forces would average out and all particles would fly almost straight through. Backward deflections are only possible when the positive charge and mass are concentrated in a small, dense nucleus.

Why you need this for the exam:

The Rutherford experiment is a classic of descriptive exam questions: be able to link rare large-angle deflections to the existence of a small, massive, positive nucleus and to the dependence of $\theta$ on $b$. Trick: small $b$ ⇒ large angle.

Remember: the scattering angle grows as the impact parameter b decreases (closer to the nucleus, stronger repulsion); all the mass and positive charge are concentrated in a small, dense nucleus.