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 104 nm and has a dielectric constant of 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 1,100 kg/m3. (Assume the volume of blood due to components other than red blood cells is negligible.) volume 1.06-15m3 surface area 6.13e-10x Your response differs from the correct answer by more than 10%. Double check your calculations. m2 (b) Estimate the capacitance of the cell by assuming the membrane surfaces act as parallel plates. 2.8e-13 X Your response differs from the correct answer by more than 10%. Double check your calculations. F (c) Calculate the charge on the surface of the membrane. 14X Your response differs from the correct answer by more than 10%. Double check your calculations. C How many electronic charges does the surface charge represent? 1.72e5 Your response differs from the correct answer by more than 10%. Double check your calculations

Answer 1

Given we know density = mass/volume v = m/d substitute given mass m = 1.10 times 10^- 12 density of blood d = 1100 v = 1.10 times 10^- 12/1100 v = 1 times 10^- 15 m^3 - (1) volume of cell is 1 times 10^- 15 m^2 surface area of red blood cells A = 4 pi r^2 - (A) we need to find radius volume = 4/3 pi r^3 r = (3 v/4 pi)^1/3 - (2) substitute (1) in (2) r = (3(1 times 10^- 15)/4 pi)^1/3 r = 6.203 times 10^- 6 m - (#) substitute (3) in (A) A = 4 pi (6.203 times 10^- 6)^2 A = 4.835 times 10^- 10 m^2 Surface Area is 4.835 times 10^- 10 m^2 thickness of membrane d = 104 nm we know c = k epsilon_0 A/d