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

Question

6) The membrane that surrounds a certain type of living cell has a surface area of 5.0 x 10 -9 m 2 and a thickness of 1.0 x 10 -8 m. Assume that the membrane behaves like a parallel plate capacitor and has a dielectric constant (?) of 5.0. a) The potential on the outer surface of the membrane is 60.0 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 potassium (K) ions (charge +e), how many such ions are present on the outer surface?

Explanation / Answer

a)

C = kA0/d

C = 5*5*10^-9*8.85*10^-12/10^-8 = 2.2125*10^-11 F

Q = 2.2125*10^-11*60*10^-3 = 1.3275*10^-12 C

b)

no. of ion = Q/e

no. = 1.3275*10^-12/1.6*10^-19 = 8.296875*106

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