A cell membrane has a surface area of 1.0 times 10 -1 m2, a dielectric constant

Question

A cell membrane has a surface area of 1.0 times 10 -1 m2, a dielectric constant of 5.2, and a thickness of 7.5 nm. The membrane acts like the dielectric in a parallel plate capacitor; a layer of positive ions on the outer surface and a layer of negative ions on the inner surface act as the capacitor plates. The potential difference between the "plates" is 90.0 mV. How much energy is stored in this capacitor ? How many positive ions are there on the outside of the membrane? Assume that all the ions are singly charged (charge +e).

Explanation / Answer

Given that the surface area of the cell membrane is A = 1.0 *10^-7 m^2 dielectric constant is k = 5.2 thickness t = 7.5 nm                    = 7.5 *10^-9 m capacitor C = k _0 A / t                       = 5.2 * 8.85*10^-12 * 1.0 *10^-7 / 7.5 *10^-9 m                      = 61.36 *10^-9 F charge of the capacitor is Q = CV                                                = 61.36 *10^-9 F   * 90.0 *10^-3 V                                                 = 5.5 *10^-9 C a ) Energy stored in a capacitor is E = 1/2 CV^2                                                           = 0.248*10^-9 J b ) positive ions outside the membrane is  Q / q                                                                 = 5.5*10^-9 C/1.6*10^-19 C                                                                  = 3.43*10^10 ions     

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