Question

A red blood cell may carry an excess charge of about -2.5×10^−12 C distributed uniformly over its surface. The cells, modeled as spheres, are approximately 8 μm in diameter and have a mass of 9.0×10^−14 kg.

1) How many excess electrons does a typical red blood cell carry? (Express your answer to two significant figures.)

2) 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. (Express your answer to two significant figures.)

3) What is the surface charge density σσ on the red blood cell? Express your answer in C/m22. (Express your answer to two significant figures.)

4) What is the surface charge density σσ on the red blood cell? Express your answer in electrons/m22. (Express your answer to two significant figures.)

Answer 1

1) No. of excess electron will be be given by total charge/charge of electron

(-2.5*10^-12/(-1.6*10^-19)) = 1.6*10⁸

2) mass of excess electron = 1.6*10⁸*9.1*10^-31 = 14.56*10^-23kg

Mass of cell with electron = 9.0*10^-14

Mass of cell without electron = 9.0*10^-14 - 14.56*10^-23

the ratio of mass of excess electrons to the mass of cell without electrons = 14.56*10^-23/(9.0*10^-14-14.56*10^-23)

= 1.6*10⁹

The ratio is quite large hence the mass of electron will not affect appreciably the total mass of cell.

3) surface charge density = total charge/ area

= (-2.5*10^-12)/(4*π*(4*10^-6)²)

= -1.2*10^-2 C/m^{​​​​​​2}

4) surface charge density in terms of electron will be given by no. of electrons divided by surface area

= no. of electrons/ area

= 1.6*10⁸/(4*π*(4*10^-6)²)

= 1.3*10²⁰ electrons/m^{​​​​​​2}