Rutherford's Alpha Particle Scattering — 3D Lab Simulation
Discovery of the dense atomic nucleus
Theoretical Foundation & Historical Context
Bombarding ultra-thin gold foil with alpha particles, Rutherford found most passed through undeflected, but roughly 1 in 8,000 bounced backwards at angles >90°. This proved atoms are mostly empty space with a tiny, positively charged nucleus at the center.
Law: Coulomb Nuclear Scattering & Atomic Architecture | Scientist: Ernest Rutherford | Year: 1911
Key Learning Objectives & Competencies
- ✓ Explain how the unexpected back-scattering of alpha particles disproved J.J. Thomson's plum pudding model.
- ✓ Calculate the distance of closest approach for central head-on collisions: r_min = 2kZe² / E_k.
- ✓ Analyze the Rutherford differential scattering cross section: dσ/dΩ ~ 1 / sin⁴(θ/2).
Mathematical Formulations & Differential Equations
F(r) = (1 / 4πε₀) · ( (2 · Z · e²) / r² )
Repulsive force between alpha particle and heavy nucleus
dσ/dΩ = ( (z · Z · e²) / (16πε₀ · E_k) )² · ( 1 / sin⁴(θ / 2) )
Scattering rate inversely proportional to sin⁴(θ/2)
d_min = (2 · Z · e²) / (4πε₀ · E_k)
Head-on collision boundary setting nuclear radius limit
Physical Parameters & Units of Measurement
| Symbol | Physical Quantity | SI Unit | Default |
|---|---|---|---|
| Z | Target atomic number (Gold = 79) | — | — |
| E_k | Alpha particle kinetic energy (MeV) | — | — |
| θ | Scattering deflection angle (°) | — | — |
Real-World & Industrial Engineering Applications
Rutherford Backscattering Spectrometry (RBS) for non-destructive thin film material characterization.
High-energy particle detector geometry in CERN Large Hadron Collider (LHC) experiments.
Radiation protection shielding calculation and alpha particle alpha-decay spectrometry.
3-Step Controlled Experimental Protocol
- Step 1: Baseline Setup — Initialize the simulation in standard conditions and observe undisturbed system dynamics.
- Step 2: Parameter Variation — Gradually modulate physical parameters using the control panel sliders.
- Step 3: Verification & Phase Space Analysis — Compare phase space trajectories and conservation metrics against analytical ODE solutions.
Frequently Asked Questions (FAQ)
What did Rutherford mean when he said 'It was as if you fired a 15-inch shell at tissue paper and it came back'?
Thomson's plum pudding model assumed positive charge was diffuse throughout the atom, which could never generate enough electric force to deflect fast alpha particles. Large back-deflections proved that the atom's positive charge is concentrated in an ultra-dense central nucleus.
What is the typical size of an atomic nucleus compared to the atom itself?
The atom's electron cloud is approximately 10⁻¹⁰ meters (1 Ångström), while the gold nucleus is only about 10⁻¹⁴ meters. The nucleus is roughly 10,000 times smaller, meaning the atom is more than 99.9999999999999% empty space.
Why doesn't the alpha particle enter the gold nucleus in low-energy experiments?
Both the alpha particle (+2e) and gold nucleus (+79e) are positively charged. The immense electrostatic Coulomb repulsive force creates a potential energy barrier that repels incoming alpha particles before nuclear strong forces can take effect.
Related Simulations & Experiments
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