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Brownian Motion: Measuring Avogadro’s Constant (Within a Few Percent) For $70 Beth Parks

Brownian Motion: Measuring Avogadro’s Constant (Within a Few Percent) For $70 Beth Parks Rebecca Metzler Colgate University. Why Brownian Motion? Historically important: Einstein’s 1905 paper Important in practice: led to accurate measurement of Avogadro’s number

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Brownian Motion: Measuring Avogadro’s Constant (Within a Few Percent) For $70 Beth Parks

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  1. Brownian Motion: Measuring Avogadro’s Constant (Within a Few Percent) For $70 Beth Parks Rebecca Metzler Colgate University

  2. 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

  3. 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 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

  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. 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

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