Experiment Data Analysis Lab

Lab Goals

The goals of this lab are to explore the statistical properties of Brownian motion and confirm the diffusion relation. Learning how to perform video-based data analysis as well as understanding device calibration is also part of this lab.

Lab Manifest

• Sample of micron-sized silicon spheres
• Digital USB microscope
• LoggerPro (for video analysis)
• Lab Handout

Background Reading

• Original article by Robert Brown (1828): Phil. Mag. 4, 161-173, 1828.
• Theory of Brownian motion by Einstein (1905): Annalen der Physik 17: 549-560 (in German).
• English translation by Einstein (published 1956): "Investigations on the Theory of Brownian Movement". New York: Dover, 1956.

See also the Brownian motion simulator for a more direct demonstration of how kinetic collisions with thermal molecules leads to Brownian motion.

General Instructions

The lab handout, linked above, gives detailed instructions for this lab. There are two main tasks for this lab, which can be done separately.

The first task is to collect data with the USB microscope which demonstrates Brownian motion of silicon microspheres in water. This data will be in the form of a time-lapse series of frames which can be saved as a movie. In addition to a chunk of raw data, some calibration data (observing a calibration plate of known dimension) is also necessary. This first step should be performed during your lab time with the equipment provided and TA supervision. Working with a lab partner is encouraged.

The second task is analyzing this data in MATLAB to elucidate the statistical properties of Brownian motion. This second task should be done on your own.

Code Assignment

There is no extra code to hand in for this lab. All information about what you have done should be included in your lab notebook.

Errata

Some further documentation on video analysis in LoggerPro is available from Vernier.