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: (a) a very small nucleus surrounded by mostly empty space (b) a nucleus containing most of the mass of the

Published by Patrick Mutisya · 8 days ago

Cambridge IGCSE Physics 0625 – 5.1.1 The Atom

5.1.1 The Atom

Objective

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:

  1. a very small nucleus surrounded by mostly empty space
  2. a nucleus containing most of the mass of the atom
  3. a nucleus that is positively charged

Background: Rutherford’s Gold‑foil Experiment

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.

Suggested diagram: Schematic of Rutherford’s gold‑foil experiment showing the source of α particles, the thin metal foil, and the surrounding detection screen.

Observations and Their Interpretation

ObservationInterpretation (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.

Evidence Explained

(a) Very small nucleus surrounded by mostly empty space

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.

(b) Nucleus containing most of the mass of the atom

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.

(c) Nucleus that is positively charged

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.

Key Formulae

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:

  • \$d\sigma/d\Omega\$ – differential cross‑section (probability of scattering into solid angle \$d\Omega\$)
  • \$Z1\$, \$Z2\$ – atomic numbers of the α particle (2) and the target nucleus
  • \$e\$ – elementary charge
  • \$E\$ – kinetic energy of the α particle
  • \$\theta\$ – scattering angle

Summary Table

EvidenceWhat it Shows About the Atom
Most α particles pass straight throughAtom is mostly empty space
Small‑angle deflectionsExistence of a small, dense region that can exert a weak repulsive force
Large‑angle / backward scatteringPresence of a very massive, positively charged nucleus

Conclusion

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.