NAME:_______________________________ 1125:201 INTRODUCTION TO BIOMEDICAL ENGINEERING, Fall 2010 Bioelectrical Phenomena Instructor:Nada Boustany HOMEWORK #2- Due THURSDAYDec. 2 Problem 1:Relationships, variables and constants:σ: conductivity in (Ω.m)-1= |z|.F.u.c Einstein relationship: D/u= (RT)/(|z| F) E= -dφ/dx J= Γ.z.F z = valence of the ion. c = concentration in moles/cm3u = mobility in cm2/volt/s D = diffusivity in cm2/s F is Faraday’s constant= 96,500 C/mole R is the gas constant = 8.31 J/mole/K T is the temperature in Kelvin (K). J is the current density in C/cm2/s φis the electrical potential in Volts Γis the molecular flux in moles/cm2/s ρ is the charge density in Coul/cm3A cell has a membrane, which is permeable only to K+. The concentrations of K+ are 5mM outside and 145mM inside. a.Using Ohm’s law, Jdrift= σE, rewrite the electrical drift current, Jdrift, for K+ as a function of mobility, concentration, the electric potential and x. b.Using Fick’s law, Γdiff= -D.dc/dx, derive the diffusion current, Jdiff, for K+ as a function of diffusivity, concentration and x. c.Assuming that K+ ions are at equilibrium, write an expression relating Jdrift to Jdiff. d.Integrate the equation found in Part c and derive an expression for the Nernst potential for K+.
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