The membrane that surrounds a certain type of living cell has a surface area of

Question

The membrane that surrounds a certain type of living cell has a surface area of 6.2 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 +77.8 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?

Please include units and round to 3 sig figs.

Explanation / Answer

a)C = k0A/d = (5.1*8.85*10^-12* 6.2*10^-9)/(1.2 *10^-8) = 2.33*10^-11

Q=CV = (2.33*10^-11)*(77*10^-3) = 1.79*10^-12 C

b)n= Q/e = (1.8*10^-12)/(1.6*10^-19) = 1.12*10^7 electrons

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