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 10-9 m2 and a thickness of 1.09 10-8 m. Assume that the membrane behaves like a parallel plate capacitor and has a dielectric constant of 5.50. (a) The potential on the outer surface of the membrane is +58.2 mV greater than that on the inside surface. How much charge resides on the outer surface? C (b) If the charge in part (a) is due to K+ ions (charge +e), how many such ions are present on the outer surface? ions

Explanation / Answer

Given that

k = 5.5

t = 1.09*10^-8 m

A = 5.1*10^-9 m^2

dV = 58.2 mV

C = k*eo*A/d

Q/dV = k*eo*A/d

Q/(58.2*10^-3) = 5.5*8.85*10^-12*5.1*10^-9/(1.09*10^-8)

Q = 1.33*10^-12 C

b) each ion has charge 1.6*10^-19 C

in 1C it has 1/(1.6*10^-19) = 6.25*10^18 ions

so in 1.33*10^-12 C,it has 6.25*10^18*1.33*10^-12 = 8.312*10^6 ions

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