Published by Patrick Mutisya · 8 days ago
Describe how the scattering of alpha (α) particles by a sheet of thin metal supports the nuclear model of the atom, by providing evidence for:
In 1909 Ernest Rutherford directed a narrow beam of α particles (helium nuclei, charge \$+2e\$, mass \$4u\$) at a very thin sheet of gold foil. A fluorescent screen surrounding the foil recorded the impact points of the scattered α particles.
| Observation | Interpretation (Evidence for the nuclear model) |
|---|---|
| \overline{96} % of α particles passed straight through the foil with little or no deflection. | Most of the atom is empty space; the α particles encounter no significant obstruction. |
| \overline{4} % of α particles were deflected at small angles. | Occasional close encounters with a concentrated positive charge cause mild repulsion, indicating a small, dense region. |
| \overline{0}.5 % of α particles were reflected backward (deflection \$>90^\circ\$). | Some α particles struck a very massive, positively charged core directly, requiring a compact nucleus with most of the atom’s mass. |
The overwhelming majority of α particles emerged undeflected. If the atom were a solid sphere of positive charge, the α particles would have been significantly slowed or stopped. The fact that they travel through almost unhindered shows that the positive charge (and most of the mass) is confined to a region far smaller than the atomic diameter.
Only a tiny fraction of α particles experienced large-angle scattering. To reverse the direction of a fast, massive α particle, the target must exert a very strong repulsive force over a very short distance. This can only be provided by a region that is both extremely dense and massive – i.e., the nucleus. The mass of the atom is therefore concentrated in the nucleus, while the surrounding electron cloud contributes negligibly to the total mass.
α particles carry a positive charge (\$+2e\$). The observed repulsion (deflection) indicates that the region they encounter also carries a positive charge. If the nucleus were neutral or negatively charged, the α particles would be attracted or pass through without deflection. The backward scattering demonstrates a strong Coulomb repulsion, confirming the nucleus’s positive charge.
The quantitative description of the scattering is given by the Rutherford scattering formula:
\$\frac{d\sigma}{d\Omega} = \left(\frac{1}{4\pi\varepsilon0}\right)^2 \frac{(Z1 Z_2 e^2)^2}{16E^2}\frac{1}{\sin^4(\theta/2)}\$
where:
| Evidence | What it Shows About the Atom |
|---|---|
| Most α particles pass straight through | Atom is mostly empty space |
| Small‑angle deflections | Existence of a small, dense region that can exert a weak repulsive force |
| Large‑angle / backward scattering | Presence of a very massive, positively charged nucleus |
Rutherford’s scattering experiment provides direct, observable evidence that an atom consists of a tiny, positively charged nucleus containing almost all of the atom’s mass, surrounded by a vast region of empty space occupied by electrons. This experimental result led to the abandonment of the “plum‑pudding” model and the acceptance of the modern nuclear model of the atom.