Evidence source in atomic structure
“How did rutherford know that the nucleus is positively charged” is answered by the behavior of alpha particles in the gold-foil scattering experiment. Alpha particles carry positive charge, and their deflections revealed the sign and concentration of charge inside atoms.
Large-angle deflection of positively charged projectiles requires a strong repulsive interaction from a concentrated positive center.
Charge sign from electrostatic interaction
Alpha particles are helium nuclei (\(\mathrm{He^{2+}}\)) and therefore have charge \(q_\alpha = +2e\). Their trajectories through thin metal foil were mostly straight, with a small fraction deflected by large angles and a very small fraction scattered nearly backward. A backward-type event is naturally produced by repulsion: the projectile approaches, slows in the electric field, and reverses direction.
The electrostatic potential energy for two point charges separated by distance \(r\) is:
\[ U(r) = \frac{1}{4\pi\varepsilon_0}\,\frac{q_\alpha\,q_N}{r} \]
For repulsion, \(U(r)\) increases as \(r\) decreases, which occurs when \(q_\alpha q_N > 0\). Since \(q_\alpha\) is positive, the scattering center’s charge \(q_N\) must also be positive.
Concentration of charge and mass
The rarity of large-angle events is as important as their existence. Most alpha particles passed through because atoms are mostly empty space at the scale of the alpha path. The occasional dramatic deflection requires a very intense electric field encountered only when an alpha particle approaches very near a compact region of charge. A diffuse positive charge spread throughout the atom (as in early “plum pudding” pictures) produces only small cumulative deflections, not sharp backscattering.
Visualization of the scattering geometry
Observations and corresponding inferences
| Observation | Electrostatic implication | Atomic-structure inference |
|---|---|---|
| Most alpha particles pass straight through the foil | Little interaction for most trajectories | Atoms are mostly empty space at the scale of the alpha path |
| A small fraction deflect by noticeable angles | Strong force acting during close approach | Charge is concentrated rather than spread uniformly |
| Very rare large-angle and near-backward scattering | Repulsive interaction with a massive, compact center | Nucleus contains positive charge and most of the atom’s mass |
Role of the alpha particle’s known charge
The positive charge of alpha particles was established independently through their behavior in electric and magnetic fields and through identification with helium ions. With \(q_\alpha > 0\), a repulsive scattering center requires \(q_N > 0\). A negative center would preferentially attract alphas, changing the qualitative pattern of close-approach trajectories and making backward-type repulsion events physically inconsistent with the observed interpretation.
Common pitfalls
- Confusion between “positive nucleus” and “positive atom,” despite neutral atoms having total charge zero.
- Electron attribution for large-angle scattering, despite electrons being too light and too diffuse to reverse an alpha particle’s direction.
- Energy-loss explanations substituted for electrostatic deflection, despite scattering angles being primarily directional changes from force, not stopping in the foil.