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 5.10 Times 10^-9 m^2 and a thickness of 9.00 Times 10^-9 m. Assume that the membrane behaves like a parallel plate capacitor and has a dielectric constant of 5.10. The potential on the outer surface of the membrane is +55.2 mV greater than that on the inside surface. How much charge resides on the outer surface? If the charge in part (a) is due to K^+ ions (charge +e), how many such ions are present on the outer surface?

Explanation / Answer

a) We have V = E/*d where E = /o

So V = /(*o)*d....so = Q/A = V*(*o)/d

So Q = A*( V*(*o)/d) = 5.10x10^-9*55.2x10^-3*5.10*8.854x10^-12/9x10^-9... = 1.4124x10^-12C

b) Charge of each K+ is 1.60x10^-19

So the number of ions = 1.4124x10^-12/1.60x10^-19 = 8.81x10^6 ions

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