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

5.1.1 The Atom

Learning objective

Describe how the scattering of α‑particles by a thin sheet of metal supports the nuclear model of the atom by giving evidence for:

  • a very small nucleus surrounded by mostly empty space,

  • a nucleus that contains most of the atom’s mass,

  • a nucleus that is positively charged.

Rutherford’s gold‑foil experiment – background

In 1909 Ernest Rutherford directed a narrow beam of α‑particles (helium nuclei, charge +2e, mass ≈ 4 u) at an extremely thin sheet of gold foil (high atomic number Z = 79). The set‑up is shown in Figure 1.

Schematic of Rutherford’s gold‑foil experiment: α‑source → collimator → gold foil → fluorescent screen

Figure 1 – Schematic of the experiment. The foil must be thin enough that most α‑particles can pass through, allowing their scattering to be observed on the circular fluorescent screen.

Typical observations (real‑world percentages)

Result (per 1000 α‑particles)Interpretation – what it tells us about the atom
≈ 960 pass straight through with little or no deflection (≈ 96 %).Most of the atom is empty space; the α‑particle encounters no significant obstruction.
≈ 40 are deflected at small angles (θ ≈ 30°, ≈ 4 %).Occasional close approaches to a compact, positively‑charged region cause mild repulsion – evidence of a tiny nucleus.
≈ 5 are reflected backward (θ > 90°, ≈ 0.5 %).Only a very massive, positively‑charged core can reverse the direction of a fast α‑particle; this shows the nucleus contains most of the atom’s mass.

Evidence explained

(a) Very small nucleus surrounded by mostly empty space

  • ≈ 96 % of α‑particles go through undeflected.

  • If the positive charge were spread throughout the atom (as in the plum‑pudding model), the particles would be slowed or stopped.

  • Therefore the nucleus must occupy only about 10⁻⁵ of the atomic volume – a region far smaller than the overall atomic diameter.

(b) Nucleus contains most of the atom’s mass

  • ≈ 0.5 % of α‑particles are reflected back (θ > 90°).

  • Reversing a fast, massive α‑particle requires an extremely strong Coulomb repulsion over a very short distance.

  • Such a force can only be produced by a region that is both very dense and very massive – the nucleus.

  • Consequently, almost all of the atom’s mass resides in the nucleus; the surrounding electron cloud contributes negligibly.

(c) Nucleus is positively charged

  • α‑particles themselves carry a +2e charge.

  • The observed repulsive deflection proves that the region they encounter also carries a net positive charge.

  • If the nucleus were neutral or negatively charged, the α‑particles would be attracted or would pass through with little deflection.

Side box – Rutherford scattering formula (A‑Level extension)

Not examined at IGCSE level – useful for curious students or A‑Level study.

\[

\frac{d\sigma}{d\Omega}= \left(\frac{1}{4\pi\varepsilon_{0}}\right)^{2}

\frac{(Z{1}Z{2}e^{2})^{2}}{16E^{2}}\,

\frac{1}{\sin^{4}(\theta/2)}

\]

  • \(d\sigma/d\Omega\) – differential cross‑section (probability of scattering into a solid angle \(d\Omega\)).

  • \(Z{1}=2\) for the α‑particle; \(Z{2}\) is the atomic number of the target nucleus (e.g., 79 for gold).

  • \(E\) – kinetic energy of the α‑particle.

  • \(\theta\) – scattering angle.

Suggested classroom activity (AO3 – experimental skills)

  1. Simulation: Use an online Rutherford‑scattering simulation (e.g., PhET “Rutherford Scattering”).

  2. Procedure:

    • Fire a fixed number of α‑particles at a virtual gold foil.

    • Record the scattering angle for each particle.

    • Classify the results into three groups:

      • Straight‑through (θ ≈ 0°),

      • Small‑angle (θ < 30°),

      • Large‑angle / backward (θ > 90°).

  3. Data handling: Calculate the percentage of particles in each group and compare with the real‑world values given above.

  4. Safety note (real experiment): If a genuine α‑source were used, students would need lead shielding, a sealed source, and strict radiation‑safety supervision. (The simulation is safe and requires no special precautions.)

  5. Reflection question: How do the percentages you obtained from the simulation differ from the observed 96 % / 4 % / 0.5 %? What experimental factors (foil thickness, α‑energy, detector resolution) could explain any discrepancy?

  6. Discussion prompts:

    • Why do most particles pass straight through?

    • What does the small‑angle scattering tell you about the size of the nucleus?

    • How does the large‑angle scattering support the idea that the nucleus contains most of the mass?

    • Why does the repulsive nature of the scattering prove a positive nuclear charge?

Summary table

Evidence from the experimentWhat it shows about the atom
≈ 96 % of α‑particles pass straight through (θ ≈ 0°)Atom is mostly empty space; the nucleus occupies only ~10⁻⁵ of the atomic volume.
≈ 4 % are deflected at small angles (θ ≈ 30°)Existence of a tiny, dense, positively‑charged nucleus that can exert a weak repulsive force.
≈ 0.5 % are scattered at angles > 90°Presence of a very massive, positively‑charged nucleus containing almost all of the atom’s mass.

Conclusion

Rutherford’s gold‑foil experiment provides clear, observable evidence that an atom consists of a tiny, positively‑charged nucleus containing almost all of its mass, surrounded by a vast region of empty space occupied by electrons. This experimental result replaced the earlier “plum‑pudding” model and established the modern nuclear model of the atom, fulfilling the Cambridge IGCSE requirement for learning objective 5.1.1.