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 4.50 10-9 m2 and a thickness of 9.80 10-9 m. Assume that the membrane behaves like a parallel plate capacitor and has a dielectric constant of 4.60.

(a) The potential on the outer surface of the membrane is +59.4 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

(a)

The capacitance of a parallel-plate capacitor is k*?0*A/d;

k = 5, A= 4.5*10^-9m, d = 9.8*10^-9 m ?0 = 8.85*10^-12 F/m

Plugging in, we get:

C = 1.87*10^-11 F

(b)

Q = V*C = 59.4*10^-3*1.87*10^-11 = 1.11*10^-12 C

The charge on each ion is e = 1.6*10^-19 C, so the number of ions is 1.11*10^-12 / 1.6*10^-19 = 6.94*10^6 ions

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