   Chapter 16, Problem 57P

Chapter
Section
Textbook Problem

A model of a red blood cell portrays the cell as a spherical capacitor, a positively charged liquid sphere of surface area A separated from the surrounding negatively charged fluid by a membrane of thickness t. Tiny electrodes introduced into the interior of the cell show a potential difference of 100. mV across the membrane. The membrane’s thickness is estimated to be 100. nm and has a dielectric constant of 5.00. (a) If an average red blood cell has a mass of 1.00 × 10−12 kg, estimate the volume of the cell and thus find its surface area. The density of blood is 1.10 × 103 kg/m3. (b) Estimate the capacitance of the cell by assuming the membrane surfaces act as parallel plates. (c) Calculate the charge on the surface of the membrane. How many electronic charges does the surface charge represent?

(a)

To determine
The volume of the cell.

Explanation

Given info: The mass (m) of the cell is 1.00×1012kg . The density of blood ( ρ ) is 1.10×103kg/m3 .

Explanation:

Formula to calculate the volume of the cell is,

V=mρ

Substitute 1.00×1012kg for m and 1.10×103kg/m3 for ρ

V=1.00×1012kg1.10×103kg/m3=9

(b)

To determine
The capacitance of the cell.

(c)

To determine
The number of electronic charges.

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