Alpha-particle scattering experiment
Geiger and Marsden fired alpha particles at thin gold foil. Most went straight through; about 1 in 8000 turned back beyond 90°, revealing a tiny, heavy, positive nucleus.
The experiment, step by step
Rutherford suggested the experiment and his assistants Hans Geiger and Ernest Marsden did it (the textbook dates it to 1911).
- 1A radioactive source, ²¹⁴₈₃Bi, kept inside a lead block, gives out alpha particles of 5.5 MeV.
- 2Narrow lead slits (a collimator) turn them into a fine, straight beam.
- 3The beam strikes a very thin gold foil, about 2.1 × 10⁻⁷ m thick.
- 4Scattered alpha particles hit a zinc sulphide (ZnS) screen. Each hit makes a tiny flash of light, called a scintillation, seen through a microscope.
- 5The screen and microscope rotate round the foil, so flashes are counted at many scattering angles θ. The whole set-up is kept in vacuum.
Observations and what they tell us
| Observation | Conclusion |
|---|---|
| Most alpha particles pass through the foil undeflected | Most of the atom is empty space |
| Only about 0.14% are scattered by more than 1° | The charge that repels them is packed into a very small region |
| About 1 in 8000 are deflected by more than 90°; a few come almost straight back | All the positive charge and nearly all the mass of the atom sit in a tiny, dense nucleus |
| The number scattered falls very steeply as θ increases | A large deflection needs a nearly head-on approach, which is rare |
Impact parameter and distance of closest approach
The path of an alpha particle depends on its impact parameter b: how far its starting line of motion is from the centre of the nucleus. A large b means the particle passes far away, so it is hardly deflected. A small b brings it close to the nucleus, where the Coulomb repulsion is strong, so it is deflected through a large angle. For a head-on approach (b = 0), the particle slows down, stops for an instant and turns back through 180°. At that point all its kinetic energy K has become electric potential energy, so K = (1/4πε₀)(2e)(Ze)/d. This gives the distance of closest approach d = (1/4πε₀) × 2Ze²/K. The nucleus must be smaller than d. The electrons of the gold atom hardly affect the alpha particle, because it is about 7300 times heavier than an electron.
Worked example: distance of closest approach
An alpha particle of kinetic energy 5.5 MeV moves head-on towards a gold nucleus (Z = 79). Find its distance of closest approach. (1/4πε₀ = 9 × 10⁹ N m² C⁻², e = 1.6 × 10⁻¹⁹ C, 1 MeV = 1.6 × 10⁻¹³ J)
- Given: K = 5.5 MeV = 5.5 × 1.6 × 10⁻¹³ J = 8.8 × 10⁻¹³ J; Z = 79.
- Formula: d = (1/4πε₀) × 2Ze²/K.
- Numerator: 9 × 10⁹ × 2 × 79 × (1.6 × 10⁻¹⁹)² = 9 × 10⁹ × 158 × 2.56 × 10⁻³⁸ = 3.64 × 10⁻²⁶ J m.
- d = 3.64 × 10⁻²⁶ J m ÷ 8.8 × 10⁻¹³ J = 4.1 × 10⁻¹⁴ m.
- So the gold nucleus is smaller than about 4 × 10⁻¹⁴ m. If K were halved, d would double.
d ≈ 4.1 × 10⁻¹⁴ m (about 41 fm)
How to draw the graph of number scattered against angle
- Draw the x-axis for the scattering angle θ, from 0° to 180°.
- Draw the y-axis for the number of alpha particles scattered, N(θ), and write (log scale) beside it.
- Plot a curve that is very high near 0° and falls very steeply as θ grows, becoming very small beyond 90°.
- Mark a few dots on the curve and label them experimental points; label the line theoretical curve (nuclear model).
- Write the title: N(θ) against θ for alpha particles on gold foil.
Scattering is still how scientists study things too small to see. Ion-beam labs fire fast particles at thin films used in solar cells and computer chips and measure how they bounce back, to check the film's thickness and purity.
2 marks: “Draw the graph of the number of alpha particles scattered against the scattering angle in the Geiger-Marsden experiment. What does it show?” Axes θ (0° to 180°) and N(θ) on a log scale; a curve falling steeply with θ. Most particles go nearly straight, very few at large angles, so the positive charge is in a tiny nucleus.
3 marks: “State three observations of the alpha-particle scattering experiment and the conclusion from each.” Most pass undeflected: atom mostly empty. About 0.14% deflect more than 1°: concentrated charge. About 1 in 8000 deflect beyond 90°: tiny, heavy, positive nucleus.
2 marks: “Define impact parameter. What is the scattering angle of an alpha particle whose impact parameter is zero?” Perpendicular distance of the initial velocity line of the alpha particle from the centre of the nucleus. For b = 0 the particle turns back: θ = 180°.
Most through, few bent, 1 in 8000 back: empty atom, tiny heavy positive nucleus.