Measuring Boltzmann’s constant using video microscopy of Brownian motion

Boltzmann’s constant k was measured by observing the Brownian motion of polystyrene spheres in water. An inexpensive monochrome CCD camera and video card were used to create a video of the spheres’ motion. After preprocessing the images, custom routines were used to examine the video and to identify and track the particles from one frame to the next. From the mean squared displacement of the particles versus time, we extracted the value of k from the slope, assuming that the drag force on an individual sphere is well modeled by Stokes’ law. By averaging over 107 particles, we obtained k=(1.415±0.04)×10−23 J/K.