a) Does the mass of the extra electrons appreciably affect the mass of the cell?

Question

a) 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.

b)What is the surface charge density on the red blood cell. Express your answer in units of C/m2 AND electrons/m2.

Given: A red blood cell carries an excess charge of -2.5 x 10^-12 C. The red blood cell sphere is 6.6 micrometers in diameter and has a mass of 9.0 x 10^-14 kg. It has 1.56 x 10^7 excess electrons.

Keep in mind that this is worth a lot of points for the sake of having asked multiple questions regarding this scenario. Thank you.

Explanation / Answer

Part A)

Mass of extra electrons = (9.11 X 10^-31)(1.56 X 10^7) = 1.42 X 10^-23 kg

The mass of the cell is given as 9 X 10^-14 kg

The ratio is 1.42 X 10^-23/9 X 10^-14 = 1.58 X 10^-10

That is .000000000158Â - so NO, the extra electrons do not factor into the overall mass of the red blood cell with any amount that matters

Part B)

The charge is (1.602 X 10^-19)(1.56 X 10^7) = -2.50 x 10^-12 c

The surface area is 4pi(3.3 X 10^-6)^2 = 1.37 X 10^-10 m^2

Surface charge density = -2.50 X 10^-12/1.368 X 10^-10 = -.0183 C/m^2

In electrons per m^2, that is...

1.56 X 10^7/4pi(3.3 X 10^-6)^2 = 1.14 X 10^17 electrons/m^2

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