A model of a red blood cell portrays the cell as a spherical capacitor, a positi
ID: 585787 • Letter: A
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 95 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.)
volume: ______ m3
surface area:_______ m2
(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
(d) How many electronic charges does the surface charge represent?
_______ charges
Explanation / Answer
the volume is V=m/p
=1.10 1012 kg/1,100 kg/m3
= 1*1015 m3
V = 4/ 3 *r^3 , the radius is r = (3V/ 4)^ 1/3
and the surface area is A = 4r^2 = 4 ( 3V /4 )^2/3
= 4 ( 3/ 4 *1 × 1015 m^3)^ 2/3
=4.84 × 1010 m^2
2.
C = 0A /d = (5.00 *8.85×1012 C^2N^1m^2 *4.54×1010 m^2 )/90×109 m=2.23× 1013 F
3.
Q = C V=2.23× 1013 F*100 × 103 V=2.23*10^-14C
4. the number of electronic charges is n = Q e = 2.23*10^-14C/ 1.60×1019 C = 1.39 × 10^5 .
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