A model of a red blood cell portrays the cell as a sphereical capacitor, a posit

Question

A model of a red blood cell portrays the cell as a sphereical capacitor, a positively charged liquid spheree of surface area A separated from the surroanding 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 98 nm and has a dielectric constant of 5.00. If an average red blood cell has a mass of 1.20 times 10^-12 kg, estimate the volume of the cell and thus find its surface area. The density of blood is 1,100 kg/m^3. (Assume the volume of blood due to components other than red blood cells is negligible.) Estimate the capacitance of the cell by assuming the membrane surfaces act as parallel plates. Your response differs from the correct answer by more than 100%. F Calculate the charge on the surface of the membrane. Your response differs from the correct answer by more than 100%. C How many electronic charges does the surface charge represent? Your response differs from the correct answer by more than 100%.

Explanation / Answer

Volume = mass/ density = 1.2*10^-12/1100 = 1.09*10^-15 kg/m3

Radius is'r', 4/3* pi*r^3 = Volume

r^3 =(3*Volume/4*pi)

r = 0.638*10^-5 m

Surface Area = 4*pi*r^2

Surface Area = 4*3.14*(0.638*10^-5)^2

Surface Area = 8.02*10^-10 m2

b)

Capacitance = epsilonA/d

Capacitance = 8.85*10^-12*8.02*10^-10/98*10^-12

C = 0.724 *10^-10 Farad

c)

Charge, Q =CV

Q = 0.724 *10^-10 * 100*10^-3

Q = 0.724*10^-11 C

d)

Number of charges = 0.724*10^-11 / 1.6*10^-19

Number of Charges = 0.452 *10^8

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