Rutherford Scattering

This is an initial pass at an interactive Rutherford scattering applet that simulates the scattering of alpha particles (helium nuclei) from a nucleus of gold. The scattering part is shown to scale [where each pixel is about 1 femtometer] but the detector location is not to scale.

(Having problems with this applet?)

You have a menu of different energies, one of which [8 MeV, the initial choice] is approximately the one at which the original Geiger and Marsden experiment was done in 1909. Rutherford later explained their results with a calculation that showed how the data were consistent with Coulomb scattering from a nucleus that was small enough that it could be treated as a point charge.

The buttons control the incident particle distribution in the beam. You can also add additional particles by clicking in the gray "beamline" area where you want a particle trajectory to appear.

The red circle is suggestive of the scattering chamber where detectors were placed to observe the scattered alpha particles. Two detectors are provided so you can repeat the experiment if you wish.

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This applet lets you see the classical trajectories (ignoring quantum mechanics) of the alpha particles and how those trajectories change with energy. In particular, you can see how Rutherford could conclude that the atomic nucleus must be smaller than some size, and how experimenters can improve on that result by going to higher energy.

The light blue lines on the right side are 50 femtometers apart to help set the scale for the realistic part of this simulation.

Version: 09 Oct 1998, 8 am -- I have to exit my browser to force loading of an updated applet.

Technical Info:

Rutherford discovered the nucleus (but did not measure its size) by analyzing scattering data assuming the probe (an alpha particle) and the target (a gold nucleus) were point charges with charge +2e and +79e respectively. Then, using classical mechanics and the Coulomb force, you can calculate what the scattering should look like in the lab and compare to data.

The equation for the distance of closest approach is, using natural units and ignoring recoil (a 2% correction here, included in my calculation):

  Z1 * Z2 * e^2       2 * 79 * 1.44 MeV fm         227.52
  -------------   =   --------------------   =   ----------  fm . 
    (1/2)mv^2               KE                   KE(in MeV)
Here fm means femtometer = 10-15 m, also written 10^{-15} m.

The "5 MeV" case gives a 46.4 fm distance of closest approach for the smallest impact parameters. The "8 MeV" case has a 29 fm distance of closest approach. This is the starting condition. The "30 MeV" case gives a 7.7 fm distance of closest approach, so the smallest impact parameters would result in some interaction with the gold nucleus, whose radius is about 5.5 fm.

Geiger and Marsden used a very energetic radioactive source for their alpha particles, the isotope Po-214 [then called RaC'] which produces alphas at 7.68 MeV with an extremely short half life. It can be obtained by chemically separating one of its parent isotopes (Pb-214?) from the Ra-226 decay chain. For this energy, the distance of closest approach is about 30 fm. Thus the precise interpretation of his experiment is that the nucleus acts like a point charge down to a size of 30 fm -- i.e. it is smaller than 30 fm.

If you go to higher energies, the classical distance of closest approach gets less. You build a small accelerator so you can get an alpha with 20 MeV, and see what happens for that case. The distribution predicted for a point charge changes with energy, as you observe with this applet, but it turns out the data still agree with the theory -- now down to about 11 fm. [Actually, you do start getting some nuclear effects due to QM tunneling about this point, if I recall correctly. That is all ancient history to me.] So you work harder on your accelerator. Finally, when the energy is up around 40 MeV, probing down to about 5 fm, you notice a big change from what was predicted. Ah hah! It has finite extent. ("It" could be either your probe or target, in this case, both.)

When you run this applet at 30 MeV, you see that some trajectories get close enough to interact with the nucleus. I have not, however, included any nuclear interaction effects on the trajectory for that case.

A separate page will be developed to help you repeat the experiment. For now I will just note that there should be 11.7 times more events in the forward detector centered at 60 degrees than in the backward detector centered at 135 degrees. The way you simulate the experiment is to set the energy at 8 MeV and use the "random beam" button to produce a series of events. Count the front and back detector hits and compare.