A model of a red blood cell portrays the cell as a spherical capacitor, a positi

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 101 nm and has a dielectric constant of 5.00.

(a) If an average red blood cell has a mass of 1.10 1012 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.)

(b) Estimate the capacitance of the cell by assuming the membrane surfaces act as parallel plates.
? F

(c) Calculate the charge on the surface of the membrane.
?C

How many electronic charges does the surface charge represent?

Explanation / Answer

a)
density = 1100 kg/m3
mass = 1.1*10^-12 Kg
so,
volume = mass / density
= (1.1*10^-12 ) /1100
= 1*10^-15 m^3 <-----Answer

use:
volume = (4/3)*pi*r^3
1*10^-15 = (4/3)*pi*r^3
r = 6.20*10^-6 m

use:
surface area = 4*pi*r^2
= 4*pi*(6.20*10^-6 )^2
= 4.84*10^-10 m^2 <------Answer

b)
A = 4.84*10^-10 m^2
d = 101 nm = 1.01*10^-7 m
K = 5

use:
C = K*ebsoleneo*A/d
=5*(8.854*10^-12)*( 4.84*10^-10 ) / (1.01*10^-7 )
= 2.12*10^-12 F
=2.12 picoFarad

c)
Q = C*V
= 2.12 microFarad* 0.1 V
= 0.212 picoCoulomb

d)
number of electron = total charge / charge of 1 electron
= 0.212*10^-12 /(1.6*10^-19)
= 1.33*10^6

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