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Unformatted text preview: NAME:_______________________________ 1 125:201 INTRODUCTION TO BIOMEDICAL ENGINEERING, Fall 2010 Bioelectrical Phenomena Instructor: Nada Boustany HOMEWORK #2- Due THURSDAY Dec. 2 Problem 1: Relationships, variables and constants: : conductivity in ( .m)-1 = |z|.F.u.c Einstein relationship: D/u= (RT)/(|z| F) E= -d /dx J= .z.F z = valence of the ion. c = concentration in moles/cm 3 u = mobility in cm 2 /volt/s D = diffusivity in cm 2 /s F is Faradays 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/cm 2 /s is the electrical potential in Volts is the molecular flux in moles/cm 2 /s is the charge density in Coul/cm 3 A cell has a membrane, which is permeable only to K + . The concentrations of K+ are 5mM outside and 145mM inside. a. Using Ohms law, J drift = E, rewrite the electrical drift current, J drift , for K+ as a function of mobility, concentration, the electric potential and x. b. Using Ficks law, diff = -D.dc/dx, derive the diffusion current, J diff , for K+ as a function of diffusivity, concentration and x. c. Assuming that K+ ions are at equilibrium, write an expression relating J drift to J diff . d. Integrate the equation found in Part c and derive an expression for the Nernst potential for K+. NAME:_______________________________ 2 e. Calculate the Nernst potential for K+. Assume the membrane is at 25 o C. f. Assuming that the electric field to be constant across the membrane, we can rewrite d /dx as / . Thus, for 0 x we can re-write: J diffusion = -D.z.F.dc/dx J drift = - |z|.F.u.c.( Nernst / ) Based on these equations, show that the concentration is an exponential function of x for 0 x ....
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This note was uploaded on 10/11/2011 for the course BIOMEDICAL 201 taught by Professor Berth during the Fall '10 term at Rutgers.
- Fall '10