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 103 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	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

How many electronic charges does the surface charge represent?

Answer 1

PART (a):

Given that:

Mass of cell, m = 1.10 x 10^-12 kg

Density, d = 1100 kg/m³

Therefore, Volume of the cell is given by:

Radius of cell can be found from the equation of volume, V = 4/3 pi r³

Therefore, Radius of the cell, r = 6.204 x 10^-6 m

Therefore, Surface area is given by:

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PART (b):

Capacitance of the cell is given by:

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PART (c):

Charge on the surface of the membrane is given by:

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PART (d):

No.of electronic charges is given by: