Glucose has in water and crosses a gap in about

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Physical foundations of the living cell · Physical foundations of the living cell

Life at Thermal Energy, Ch Random walks, diffusion and the crowded cell

Problem

Glucose has

D = 6.7\times10^{-10}\,\mathrm{m^2\,s^{-1}}

in water and crosses a

1\,\mathrm{\mu m}

gap in about

0.75\,\mathrm{ms}

. A student reasons: "a

1\,\mathrm{mm}

gap is a thousand times longer than

1\,\mathrm{\mu m}

, so glucose must take a thousand times longer to cross it: about

0.75\,\mathrm{s}

." ((a)) Compute the actual time for glucose to diffuse across

1\,\mathrm{mm}

. ((b)) State the factor by which this estimate is wrong, and identify the error in the reasoning.

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