A model of a red blood cell portrays the cell as a sphericalcapacitor, a positiv

Question

A model of a red blood cell portrays the cell as a sphericalcapacitor, a positively charged liquid sphere of surface areaA separated from the surrounding negatively charged fluidby a membrane of thickness t. Tiny electrodes introducedinto the interior of the cell show a potential difference of 100 mVacross the membrane. The membrane's thickness is estimated to be100 nm and has a dielectric constant of5.00. (a) If an average red blood cell has a mass of1e-12 kg, estimate the volume of the celland thus find its surface area. The density of blood is 1100kg/m3. volume = 1 m3 surface area = 2 m2
(b) Estimate the capacitance of the cell by assuming the membranesurfaces act as parallel plates.
3 F

(c) Calculate the charge on the surface of the membrane.
4 C

How many electronic (elementary) charges does the surface chargerepresent?
5 (a) If an average red blood cell has a mass of1e-12 kg, estimate the volume of the celland thus find its surface area. The density of blood is 1100kg/m3. volume = 1 m3 surface area = 2 m2
(b) Estimate the capacitance of the cell by assuming the membranesurfaces act as parallel plates.
3 F

(c) Calculate the charge on the surface of the membrane.
4 C

How many electronic (elementary) charges does the surface chargerepresent?
5 volume = 1 m3 surface area = 2 m2

Explanation / Answer

m=1.0e-12 P=1100 V=100mV d=100nm K=5 1) V=m/P    V=(1.0e-12)/1100=9.09e-16m^3 2)V=(4/3)r^3       r^3=3V/4    r=[3(9.09e-16)/4]^1/3=6.01e-6m^2 3) C=KA/d        =(5.00)(8.85e-12)(6.01e-6)/(100e-9)=2.66e-9 4) Q=C(V)       =(2.66e-9)(100e-3)=2.66e-10 5) n=Q/e      =(2.66e-10)/(1.6e-19)=1.66e9 I hope the calculations are right. Please rate if right

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