Measuring Avogadro’s Constant (Within a Few Percent) Brownian Motion: Measuring Avogadro’s Constant (Within a Few Percent) For $70 Beth Parks Rebecca Metzler Colgate University Discovered by Robert Brown in 1827, observing motion of pollen grains.

Historically important: Einstein’s 1905 paper Why Brownian Motion? Historically important: Einstein’s 1905 paper Important in practice: led to accurate measurement of Avogadro’s number Connect microscopic and macroscopic: PV = nMRT to Brownian motion was one of the fourpapers in Einsten’s annus mirabilis: On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat, and Initial measurements of Avogadro’s number were made using viscosity. Both Brownian motion and viscosity are sensitive to the size of atoms due to their sensitivity to collision rates.

Solution: (assume a random force; yields a random walk) Force equation: Solution: (assume a random force; yields a random walk) Γ = 6πηa where η = viscosity = 1.02 × 10-3 Pa-s and a = radius of sphere “Einstein, Perrin, and the reality of atoms: 1905 revisited” Ronald Newburgh, Joseph Peidle, Wolfgang Rueckner American Journal of Physics 74 6, June 2006

Equipment: Celestron LCD Digital Microscope (need 40x zoom, or about 0.25 μm/pixel) Polysciences polystyrene microspheres 1 μm diameter ($115—concentrated solution) Saline solution for contact lenses (dilution) Dimpled slides (Fisher Scientific, $8.40/box of 12) Coverslips Coverslip placement Calibration: Borrow a calibrated slide from biology, or photograph a diffraction grating. 120 mm

Download ImageJ, available freely from NIH.

Calibrate using a known distance.

Take a series of photos spaced by 2 - 4 seconds and upload them onto the computer.

Upload files to ImageJ. Click on a sphere to follow it between successive images. Positions are automatically collected in a table.

Calculate the squared displacement between photographs. (or every other photograph, or every third, . . . ) Solve to find Avogadro’s number.

Beth Parks, Colgate University, meparks@colgate.edu Implementation summary: Equipment: Celestron LCD Digital Microscope (need 40x zoom, or about 0.25 μm/pixel) Polysciences polystyrene microspheres 1 μm diameter ($115—concentrated solution) Saline solution for contact lenses (dilution) Dimpled slides (Fisher Scientific, $8.40/box of 12) Slide covers ImageJ, available from NIH “Einstein, Perrin, and the reality of atoms: 1905 revisited” Ronald Newburgh, Joseph Peidle, Wolfgang Rueckner American Journal of Physics 74 6, June 2006 Beth Parks, Colgate University, meparks@colgate.edu