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 7.6 μm in diameter and with a mass of 9.0×10−14 kg. How many excess electrons does a typical red blood cell have? excess electrons: 1.56 ×10 7 electrons 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. ratio: 1.58 ×10 −10 What is the surface charge density on the red blood cell? Express your answer in units of C/m2 and electrons/m2. surface change density: −3.44 ×10 3 C/m2 surface charge density: 2.15 ×10 22

Answer 1

The number of excess electrons on a red blood cell =
`\rm 1.56* 10^7\ electrons.`

The ratio of the mass of the extra electrons to the mass of the cell without the excess charge =
`\rm 1.58* 10^(-10).`

The surface charge density on the red blood cell =
`\rm -1.38* 10^(-2)\ C/m^2.` =
`\rm 8.68* 10^(16)\ electrons/m^2.`

Step-by-step explanation:

Given:

• Excess charge on the red blood cell,
  `\rm q=-2.5* 10^(-12)\ C.`

• Diameter of the red blood cell,
  `\rm D = 7.6\ \mu C = 7.6* 10^(-6)\ C.`

• Mass of the red blood cell,
  `\rm m = 9.0* 10^(-14)\ kg.`

Finding the number of excess electrons on a red blood cell:

Charge on an electron,
`\rm e = -1.6* 10^(-19)\ C.`

If there are n number of excess electrons on the RBC, then,

`\rm q=ne\\\therefore n = \frac qe=(-2.5* 10^(-12))/(-1.6* 10^(-19))=1.56* 10^7\ electrons.`

Calculating the ratio of the mass of the extra electrons to the mass of the cell without the excess charge:

Mass of 1 electron,
`\rm m_e=9.11* 10^(-31)\ kg.`

Mass of n electrons,
`\rm M= n* 9.11* 10^(-31)=1.56* 10^7* 9.11* 10^(-31)=1.42* 10^(-23)\ kg.`

The ratio of the mass of the extra electrons to the mass of the cell without the excess charge is given as

`\rm Ratio = (M)/(m)=(1.42* 10^(-23))/(9.0* 10^(-14))=1.58* 10^(-10).`

Thus, the mass of the extra electrons does not appreciably affect the mass of the cell.

Calculating the surface charge density on the red blood cell:

It is given that the red blood cells can be modeled as spheres, then, the surface area of the RBC is given as

`\rm A = 4\pi (Radius)^2=4\pi * \left ( \frac D2\right ) ^2=4\pi * \left ( \frac {7.6* 10^(-6)}2\right ) ^2=1.81* 10^(-10)\ m^2.`

The surface charge density of the RBC is given as:

`\rm \sigma = \frac qA=(-2.5* 10^(-12))/(1.81* 10^(-10))=-1.38* 10^(-2)\ C/m^2.`

In terms of
`\rm electrons/m^2`,

`\sigma = \rm (n)/(A)=(1.56* 10^7)/(1.81* 10^(-10))=8.68* 10^(16)\ electrons/m^2.`