A model of a red blood cell portrays the cell as a spherical capacitor -- a posi

Question

A model of a red blood cell portrays the cell as a spherical capacitor -- a positively charged liquid sphere of surface area A separated from the surrounding negatively charged fluid by a membrane of thickness t. Tiny electrodes introduced into the interior of the cell show a potential difference of 100 mV across the membrane. The membrane's thickness is estimated to be 97 nm and its dielectric constant is 5.00.

(a) If an average red blood cell has a mass of 1.10 10-12 kg, estimate the volume of the cell and thus find its surface area. The density of blood is 1100 kg/m3.
volume= ? m3
surface area= ? m2
(b) Estimate the capacitance of the cell.
F
(c) Calculate the charge on the surface of the membrane.
C
How many electronic (elementary) charges does the surface charge represent?

Explanation / Answer

a) Volume of the cell is V = m/? = (1.1 x 10^-12 kg)/(1100 kg/m3) = 1.0 x 10^-15 m3 But V = 4/3 p r^3 (1.0 x 10^-15 m3) = 4/3 p r^3 The radius of the cell is r = 6.203 x10^-6 m The surface area is S = 4p r^2 = 4p (6.203 x10^-6 m)^2 = 4.835 x10^-10 m2 b) Thecapacitance of the cell by assuming the membrane surfaces act as parallel plates C =k Aeo/d =k (pr^2)eo/d = (5.00)(p(4.835 x10^-10 m2)^2)(8.85 x 10^-12 C2/N.m2)/(98 x 10^-9 m) =----- F c) The charge on the surface of the membrane is q = CV Here V = 100 x 10^-3 V d) The number of charges are N = q/e Here e =1.6 x 10^-19 C Substitute the values we get the answer.

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