Question

(b) A dru A drug particle has a diameter of 3 nm. The release of the drug is considered as a point source and the drug is assumed to undergo 1D diffusion. (i) Estimate the diffusion coefficient of the drug in water at room temperature. (ii) How long would it take for the drug to first reach a point 1 cm from where it was released [5]

Answer 1

This is a problem based on Einstein's theory of brownian motion of a suspended particle. The detailed solution of the.problem is follows:

Given; Diameter of the particle, d= 3 nm As the drug is considered a point yource, and assumed to undergo ID diffusion, Einstein's theory of Brownian motion predicts that AX ( t) - V2Dt - where Au(t) is the mean-square displace- ment (MSD) of a free brownian particle in ID during time t and D is the diffusion constant. (1) Diffusion coefficient (D) can be calculated by D = kg I - (11) where ke is the Baltzman constant, T is the temperature and y=6th R is the stokes friction coefficient R=d12 = 3410-9m water = 0.89 x15pa-s at T= 298 K (room) Y=643144 0.89x163x34x169 = 25:1581012ams room Now, Diffusion coefficient D = { kg = 1:38 81523 m² kg (ii) T= 298 K D = 1.38x1623x298 m2/8 = 163 xló lomils 25.15% 16-12 > D= 163 X tále my land From Eq" (11), Ax (+) = 1207 { Given that sul t) = 1x16?m, t= ?? putting values in the equation , 1X102-V2X163x10 toxt > t = - 10-4 sen 2x1.63x10 - 10 second . Ans. > t = 306748 Second A = 85.2 hours Hence it would take 85.2 hours for the drug to first reach a point I cm from where it was released