brownian motion: measuring avogadro’s constant (within a few percent) for $70 beth parks
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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 - PowerPoint PPT PresentationTRANSCRIPT
Brownian Motion: Measuring Avogadro’s Constant
(Within a Few Percent) For $70
Beth ParksRebecca Metzler
Colgate University
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
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K =32kBT
Force equation:
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md2 r r
dt2=
r Fext−Γ
d r r
dt
Solution: (assume a random force; yields a random walk)
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Rxy2 =4RTt
ΓNA
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
Calibration: Borrow a calibrated slide from biology, or photograph a diffraction grating.
120 m
Coverslip placement
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.
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Rxy2 =4RTt
ΓNA
NA = 4RT
Rxy2 Γ
t
Calculate the squared displacement between photographs.(or every other photograph, or every third, . . . )
Solve to find Avogadro’s number.
“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, [email protected]
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 coversImageJ, available from NIH
Implementation summary: