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 4.60 times 10-9 m2 and a thickness of 1.11 times 10-8 m. Assume that the membrane behaves like a parallel plate capacitor and has a dielectric constant of 5.60. (a) The potential on the outer surface of the membrane is +65.4 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?

Explanation / Answer

capaciatnce of qa parallel palte caapcitor is C = ke0A/d

where k is dieelctric constant = 5.6

e0 = permittiivty constant = 8.85*10^-12

A   = area = 4.6 *10^-9 m^2

d = thickness = 1.11*10^-8

so now C = 5.6 * 8.85*10^-12 * 4.6*10^-9/(1.11*10^-8)

C = 2.05*10^-11 F

so charge Q, capaciatnce C and voltage V are rel;ated by the formula

Q= CV

Q = 2.05*10^-11* 0.0654 = 1.34 pC

noe q= ne

n = 1.34*10^-12 /1.6*10^-19 = 8,375 *10^6 ions

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