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

Question

A red blood cell typically carries an excess charge of about -2.5 * 10^-12 distributed uniformly over its surface. The red blood cells can be modeled as spheres approximately 7.6 mu m in diameter and with a mass of 9.0 x10-^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 blood cell Express your answer in units of C/m^2and electrons/m^2.

Explanation / Answer

1) Number of charges = 2.5*10^-12 C

Excess of electrons = 2.5*10^-12 / 1.6*10^-19 C = 1.56*10^7

2)

Mass of these number of electrons is 1.56*10^7*9.31*10^-31 = 14.54*10^-24 Kg

Ratio of masses is 14.54*10^-24/ 9*10^-14 = 1.616*10^-10

3)

Surface charge density = charge/area

charge/4pi*r^2

Surface charge density = charge/4pi*r^2 = 2.5*10^-12/4*3.14*3.8^2*10^-12 =0.055/4 = 0.0137 C/m2

In terms of number of electrons ,

Surface charge density = charge/4pi*r^2 = 1.56*10^7/3.14*3.8^2*10^-12 =0.0086*10^19 electrons/m2

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