The first accurate estimate of the thickness of biological cell membranes used a

Question

The first accurate estimate of the thickness of biological cell membranes used a capacitive technique, in which the capacitance per unit area of cell membrane was determined through a macroscopic measurement of the electric properties of a suspension of cells; the result was a value of about 1 micro Faraday/cm^2 for a wide range of cells.

Question:
Assuming a dielectric constant of about 3 for the membrane material, find the membrane thickness. Note: Your answer is the thickness of the bipolar lipid layer alone, and is lower by a factor of about 3 than values based on X-ray techniques; the full membrane may be thicker still.
Express your answer using two significant figures.

Explanation / Answer

Let A be the area of each plate. Let d be the separation between plates. Let k dielectric constant. Capacitance of capacitor is           C = k oA/d            d =  k oA/ C            d = (3) (8.85x10-12 F/m)(10-4 m2)/ (1.0x10-6F)               = 26.55x10-10 m               = 2.65 nm          

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