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 · 14 days ago

Cambridge IGCSE Physics 0625 – 5.1.1 The Atom

5.1.1 The Atom

Rutherford Scattering Experiment

The experiment involved directing a narrow beam of positively‑charged alpha (α) particles at an extremely thin sheet of gold foil.

A fluorescent screen surrounding the foil recorded the deflection angles of the particles.

How the Results Support the Nuclear Model

  1. Very small nucleus surrounded by mostly empty space

    Most α‑particles passed straight through the foil with little or no deflection, indicating that the majority of the atom is empty space. Only a very small fraction were scattered at large angles, implying that a tiny, dense region caused the strong repulsive force.

  2. Nucleus contains most of the mass of the atom

    The large-angle scattering required a very massive target to change the momentum of the fast α‑particles. Since the α‑particle mass is comparable to that of a helium nucleus, the scattering centre must be much heavier than the surrounding electrons, showing that the mass is concentrated in the nucleus.

  3. Nucleus is positively charged

    α‑particles are positively charged (+2e). The observed repulsion (deflection away from the centre) can only occur if the scattering centre also carries a positive charge. The magnitude of the deflection matched calculations assuming a charge of approximately +Ze, where Z is the atomic number.

Key Observations and Quantitative Evidence

ObservationInterpretationSupporting Equation
\overline{96}% of α‑particles pass through undeflectedAtom is mostly empty space\$\displaystyle P{\text{undeflected}} \approx 1 - \frac{2\pi Z e^2}{mv^2 b{\text{min}}}\$
\overline{4}% scattered at small anglesWeak electric field from electrons\$\displaystyle \theta \approx \frac{Ze^2}{2\pi\varepsilon_0 mv^2 b}\$
\overline{0}.5% scattered at angles > 90°Direct hit on a dense, massive, positively charged nucleus\$\displaystyle \theta = \pi - 2\arctan\!\left(\frac{b}{a}\right)\$ where \$a = \frac{Ze^2}{4\pi\varepsilon_0 mv^2}\$

Conceptual Summary

  • The atom consists of a tiny nucleus (radius ≈ \$10^{-15}\,\text{m}\$) containing nearly all its mass and positive charge.
  • Electrons occupy the remaining volume (radius ≈ \$10^{-10}\,\text{m}\$), creating a region of mostly empty space.
  • The scattering pattern directly confirms the existence, size, mass, and charge of the nucleus, forming the basis of the modern nuclear model of the atom.

Suggested diagram: Schematic of the Rutherford scattering setup showing the α‑particle source, gold foil, and fluorescent detection screen with angles marked.