A bead of radius in water ( )

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Biophysics & Medical Physics · Physical foundations of the living cell

Forces, Machines and Signals, Ch Numbers and noise in a small system

Problem

A bead of radius

0.5\,\mathrm{\mu m}

in water (

\eta = 1.0\,\mathrm{mPa\,s}

), tethered by a single protein linker, is observed at

298\,\mathrm{K}

to fluctuate about its mean position with an rms amplitude of

3.2\,\mathrm{nm}

. Assume the linker behaves as a Hookean spring and that equipartition applies. ((a)) Find the effective stiffness

\kappa

of the linker. ((b)) Taking the drag on the bead as

\zeta = 6\pi\eta a

, find the relaxation time

\tau = \zeta/\kappa

with which a small displacement of the bead dies away.

Browse the problem library