Geiger and Marsden - were two young physicists in 1909
working under the supervision of Earnest Rutherford. 
Together
they did, what was has subsequently been enshrined, as a classic
experiment in the
development of twentieth century physics. [A picture of Geiger
can be found on the web, but at the time of writing no picture
of Marsden (who was a graduate student in 1909) seems to exist.]
The photo at right is of Rutherford.
Click the page at right for a copy of the complete original paper.
The revolution in thinking that followed the careful analysis of the results of this simple procedure was quite remarkable. Rutherford himself stated, "It was quiet the most incredible event that has ever happened in my life. It was almost as incredible as if you fired a 15-inch shell at piece of tissue paper and it came back and hit you." Two years later, Rutherford had realized that most of the particles that passed through the foil encountered empty space. The particles that deviated slightly were deflected by the inverse square Coulomb repulsion of like charges, and the major deflections were due to head on collisions.
Rutherford's co-workers and students had been studying the scattering of beta particles by metal foils and had by 1909 turned their attention to heavier, more energetic, alpha particles. They had a sample of radium which, with its daughter nuclei, was emitting a steady stream of alpha particles, of three different energies. [The energy of alpha particles comes from Coulomb (electrostatic) repulsion and is the same for all particles from the same decay. ]
Gold can be beaten into sheets 10-7 meters thick. Since atoms in the gold lattice are ~10-10 meters apart, the sheet is about 1000 atoms thick. The radius of closest approach for alpha particles incident on the gold is ~5x10-14 meters. If all the atoms in the gold leaf were laid on a two dimensional surface, alpha particles would pass through most of the time, unless they made a direct hit or passed very close to a nucleus (note the faint blurring of the one pixel images representing the nuclei). Since the foil is three dimensional, many atoms are behind others. The view of the gold foil that a pilot, the size of an alpha particle, would see on approach, is more like this diagram. Almost all of the alpha particles pass straight through undeflected.
Note: Geiger reported using gold foil only 400 atoms thick, (beaten as thin as possible). The foil was so delicate that it was mounted on glass. to quote Geiger and Marsden, "Different numbers of these foils were used as reflectors. Each foil was equivalent in stopping power to about 0.4 mm. of air. It was necessary to mount the foils on glass plates, but the number reflected from the glass itself was found to be very small, compared even with the number from one gold foil."
The experiment was simplicity itself. Alpha particles from the natural decay of radium were allowed to hit the foil. The experimenters looked for tiny flashes on a cylindrical scintillation counter, (a ZnS screen), which surrounded the target foil.
"By means of a low power microscope, the number of scintillations per minute on a definite square millimeter of the screen was counted for reflectors of different materials. Care was taken that the different reflectors [foils] were always placed in exactly the same position."
In addition to scattering at the expected angles they found a few very large deflections - an occasional alpha particle came straight back! It was like seeing a truck thrown off course by a chicken. They initially thought there must be impossibly strong magnetic fields in the foil but slowly, they came to realize, that atoms are mostly empty space, with tiny dense nuclei of high positive charge. They were seeing repulsion between two tiny, massive, electric charges. They had discovered the nucleus. They changed forever our concept of the atom.
Rutherford was able, over the next two years, to deduce the size of the gold nucleus and the nature of the force law (inverse square) from the 360 degree distribution of scattering angles.
Rutherford's new model of the atom was an improvement on existing ideas but still left much to be explained. (See 'Bhor' in the Quantum index). It is interesting to remember that, at the time, the neutron was unknown. We had to wait until Chadwick demonstrated the existence of the neutron in 1932.
Two alpha particles with different energies, from the decay of different heavy nuclei are diagramed at right. The points of closest approach are related to both the energy of the alpha particles and the charge of the target nucleus. The KE is equal to the PE gained given by....
If the energy of an alpha particle is 5.5 MeV, the distance of closest approach to a gold nucleus (atomic number 79) is given by....
Equal energy alpha particles are scattered by a gold nucleus. Most (not shown) are deflected less or not at all. The reduction in KE close to the target is more noticeable for closer approaches and greater deflections. The total particle energy KE+PE remains constant. The target nucleus is embedded in a crystal lattice and is taken to be stationary.
Alpha particle detection in air