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 6.2 times 10-9 m2 and a thickness of 1.9 times 10-8 m. Assume that the membrane behaves like a parallel plate capacitor and has a dielectric constant of 5.4. (a) The potential on the outer surface of the membrane is +89.6 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

As we know that in Parallel plate capacitor

C = kEpsilon*A/d

=(5.4*8.852*10^-12*6.2*10^-9)/(1.9*10^-8)

= 1.56*10^-11 F

As we know

Q = C*DeltaV

= (1.56*10^-11)*(89.6*10^-3)

= 1.39776*10^-12 C

No of Ions = (1.39776*10^-12)/(1.6*10^-19)

= 8736000 = 8.736*10^6 ions

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