RMS/Mean Free Path
Properties of Matter

Photograph of marbles in motion

Practical Activity for 14-16 PRACTICAL PHYISCS


A difficult exercise, photographing marbles to show the differences in their path lengths between collisions.

Apparatus and Materials

  • Two-dimensional kinetic model kit
  • Lamp
  • Camera

Health & Safety and Technical Notes

This kit may be obtained from science apparatus suppliers. It consists of a set of shallow trays (preferably fitted with a thin cork sheet on the base to reduce the noise-level) and a dozen or so marbles, all bar one of the same colour.

In this experiment, the tray should be placed flat on the bench top and illuminated strongly by the lamp. Arrange the lamp in such a way that most of the light entering the lens comes from the light reflected by the marbles only and not from the lamp and other reflected light. The camera must be held rigidly over the tray. An exposure must be chosen so that it shows the motion of each marble as a blur.

Read our standard health & safety guidance


  1. Agitate the tray, keeping it flat on the surface, and take a photograph.
  2. Keep the exposure time relatively short so that the motion of the marbles before collisions is shown as a blur. Use the length of the blur to estimate the distribution of velocities.
  3. If the exposure time is longer, an estimate may be made of the distribution of path-lengths between collisions.

Teaching Notes

  • This experiment is not recommended except to an enthusiast, student or teacher, who wishes to experiment with exposures.
  • If a number of photographs are taken, you can plot histograms of speed or path-length. This would show many marbles moving with speeds close to the average, some much slower and some much faster. (Path-lengths would show a similar pattern.)
  • An enthusiast could experiment with short video sequences with a digital camera.

This experiment was safety-tested in August 2006

RMS/Mean Free Path
can be analysed using the quantity RMS Speed
is used in analyses relating to Brownian Motion
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