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 6.4 x 10-9 m2 and a thickness of 1.2 x 10-8 m. Assume that the membrane behaves like a parallel plate capacitor and has a dielectric constant of 5.2. (a) The potential on the outer surface of the membrane is +54.6 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? Please write out steps and equations used! Thanks

Explanation / Answer

a) total capacitance = (5.2 * 8.854x10-12 * 6.4 x 10-9)/1.2 x 10-8

                                                = 245.55 * 10-13 F

      charge resides on the outer surface = 54.6 *10-3 * 245.55 * 10-13

                                                                  = 1.34 * 10-12 C

b) such ions are present on the outer surface = 1.34 * 10-12/1.6 *10-19

                                                                                                      = 8.375 *106

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