Geiger-Marsden Experiment

Purpose

• Rutherford suggested an experiment on the scattering of alpha particles by atoms in order to find out how charge and mass are distributed inside an atom. It was performed by his colleagues Geiger and Marsden between 1908 and 1913.
• Alpha particles are helium nuclei; they are positively charged, carrying the charge of two protons, $+2e$.

Experimental arrangement (diagram in words)

• A radioactive source of alpha particles is placed behind a collimator, i.e. a lead block with a narrow channel, so that the particles emerge as a narrow parallel beam.
• The collimated beam falls on a thin gold foil placed in its path.
• A screen coated with zinc sulphide surrounds the foil; a scattered alpha particle striking it produces a small flash of light called a scintillation.
• The scintillations are observed through a microscope which can be moved round the foil so as to cover different angles $\theta$ with respect to the direction of the incident beam.
• Label on the diagram: source, collimator, gold foil, the undeviated straight-through direction, a scattered path making the scattering angle $\theta$, the surrounding scintillation screen and the movable microscope.

Observations

• Most of the alpha particles passed straight through the foil, undeflected.
• A few were deflected, i.e. scattered, through various scattering angles.
• Only about $0.14\%$ of the incident alpha particles were scattered through angles larger than $0.1^\circ$; even out of these, most were deflected through very small angles.
• About one alpha particle in $8000$ was deflected through an angle larger than $90^\circ$, and fewer still were deflected through angles as large as $180^\circ$, that is, straight back.

Conclusions

• The atom is mostly empty space, which is why most alpha particles pass through undeviated.
• The particles that come back must have met a very massive, highly positively charged object; because so few come back, that object must occupy a very small part of the atom.
• That object is the nucleus: its size came out as about $10\ \text{fm}$, roughly $10^{-5}$ times the size of the atom, so about $10^{-15}$ of its volume.

The related numerical: distance of closest approach

• When an alpha particle moves directly towards a nucleus, its kinetic energy is steadily converted into electrostatic potential energy, and it stops when all of it has been converted.

$$K = \dfrac{1}{4\pi\varepsilon_0}\dfrac{(2e)(Ze)}{r_1+r_2}$$

• $Z$ is the atomic number of the target nucleus ($Z = 79$ for gold), and $r_1$, $r_2$ are the radii of the target nucleus and the alpha particle, so that $r_1 + r_2$ is their centre-to-centre distance when the alpha particle just touches the surface.
• Worked standard result: for an alpha particle of radius $1.80\ \text{fm}$ just reaching the surface of a gold nucleus of radius $6.23\ \text{fm}$, $K = 4.533\times10^{-12}\ \text{J} = 28.33\ \text{MeV}$.