Question

An average cylindrical axon has a cell wall that is thick and has a radius. The dielectric constant of the lipid bilayer. Find the capacitance of the axon cell wall membrane for an axon of length 9 cm. You may consider the cell membrane as having the geometry of a parallel plate capacitor by unrolling the cylinder, which yields parallel capacitor plates with an area where L is the length of the axon. Give your answer to the nearest nanofarad where 1 nanofarad = 1x10-9 F.

Answer 1

The capacitance of the axon cell wall membrane is determined using the parallel plate capacitor formula, taking into account the area of the unrolled cylindrical axon and its thickness, and is presented in the nearest nano-farad.

Step-by-step explanation:

The capacitance of the axon cell wall membrane can be found by applying the formula for the capacitance of a parallel plate capacitor, which is C = ε0 εr A / d, where ε0 is the vacuum permittivity, εr is the dielectric constant of the membrane, A is the area of the plates (unrolled cylindrical surface), and d is the thickness of the membrane. The unrolled surface area A of the cylindrical axon with length L and radius r is given by A = 2πrL. For a membrane that is 9.00 nm thick, with a given length of 9 cm, and assuming the radius and dielectric constant are provided, once the values are inputted into the capacitance formula and the result is converted to nano-farads (1 nF = 1x10-9 F), we can find the requested capacitance to the nearest nano-farad.