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Brownian Motion: Measuring Avogadro’s Constant (Within a Few Percent) For $70 Beth Parks PowerPoint Presentation
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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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slide1

Brownian Motion:

Measuring Avogadro’s Constant (Within a Few Percent)

For $70

Beth Parks

Rebecca Metzler

Colgate University

slide2

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
slide3

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

slide4

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

slide8

Upload files to ImageJ.

Click on a sphere to follow it between successive images.

Positions are automatically collected in a table.

slide9

Calculate the squared displacement between photographs.

(or every other photograph, or every third, . . . )

Solve to find Avogadro’s number.

slide10

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