A red blood cell typically carries an excess charge of about -2.5*10^-12 C distr

Question

A red blood cell typically carries an excess charge of about -2.5*10^-12 C distributed uniformly over its surface. The red blood cells can be modeled as spheres approximately 7.0 mu m in diameter and with a mass of 9.0*10^-14 kg. How many excess electrons does a typical red blood cell have? Does the mass of the extra electrons appreciably affect the mass of the cell? To find out, calculate the ratio of the mass of the extra electrons to the mass of the cell without the excess charge. What is the surface charge density on the red cell? Express your answer in units of C?m^2 and electrons/m^2

Explanation / Answer

(a) Charge on one electron=-1.6*10-19C

excess electrons=-2.5*10-12 /-1.6*10-19

=1.5625*107 electrons

(b) mass of each electron= 9.11 x10-31 kg

total mass of excess electrons= 1.5625*107 (9.11 x10-31 ) = 1.423x10-23 kg

mass of cell= 9x10-14 kg

so ratio= Me /Mc = 1.423x10-23 / 9x10-14 = 1.58 x10-10

the ratio is very small.so the mass of electrons does not affect the mass of cell appreciably.

(c)Diameter of cell= 7um = 7x10-6 m

radius of cell= 3.5 x10-6 m

surface area of cell= 4 pi r2 = 4(3.14)(3.5 x10-6 )2 = 1.54x10-10 m2

surface charge density = 2.5x10-12 /(1.54x10-10 ) = 0.0162 c/m2

in terms of electrons, surface charge density =1.5625*107 /1.54x10-10 =1.015 x1017 electrons/ m2

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