1. 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.

2. 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.

3. 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

4. Equipment:
Celestron LCD Digital Microscope
(need 40x zoom, or about 0.25 μm/pixel)
Polysciences polystyrene microspheres 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

5. Download ImageJ, available freely from NIH.

6. Calibrate using a known distance.

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

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

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

10. 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 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,