The membrane that surrounds a certain type of living cell ha

The membrane that surrounds a certain type of living cell has a surface area of 4.4 x 10-9 m2 and a thickness of 1.2 x 10-8 m. Assume that the membrane behaves like a parallel plate capacitor and has a dielectric constant of 5.1. (a) The potential on the outer surface of the membrane is +61.1 mV greater than that on the inside surface. How much charge resides on the outer surface? (b) If the charge in part (a) is due to K+ ions (charge +e), how many such ions are present on the outer surface?

Solution

A. Q = CV

V = 61.1*10^-3 V

C = k*e0*A/d = 5.1*8.85*10^-12*4.4*10^-9/(1.2*10^-8) = 1.65*10^-11 F

Q = 61.1*10^-3*1.65*10^-11 = 1.008*10^-12

Q = 1.008*10^-12 C

B. no. of ions = C/e = 1.008*10^-12/(1.6*10^-19) = 6.3*10^6

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