Can you guys please show th calciulations of how the etext arrived at certain answers. Most of the numbers were plug in out of no where without a calculation of how it is gotten.Please show a solved calcuclation

Thanks

Example 25.12 Finding the resistance and resistivity of a cell membrane Researchers use microelectrodes to measure the ion currents into and out of cells. When a neuron is in its resting state, the current into a 1mmlong segment of its 5pm-diameter axon is z 3 nA. a. What are the equivalent resistance and the resistivity of the axon's membrane? b. Measuring individual ion leak channels is difcult, but it's thought that the current through each channel is z 0.1 pA. How many leak channels are in this lmm-long segment? What is their density in channels per ,umz? PREPARE The membrane of an axon, as seen in Figure 25.41 ID, is a thin-walled cylindrical shell that has radius R, length L, and thickness d. We can imagine unrolling the cylinder to obtain a thin, at sheet of membrane of width 271R (the cylinder's circumference), length L, and thickness d. Vmem is the potential difference across this sheet, and current I passes through from outside the cell to inside. We know from Chapter 24E that the resistance of a conductor of thickness d and cross-section area A is R = pd/A, where p is the resistivity. a. We can use Ohm's law to calculate the equivalent resistance of the membrane: Rmem I Vmem 0.070 V ~ 2 X 10' 2 = 20 MQ 3 X 10-9 A The data are not precisely known, so one-significant-figure answers are appropriate. The membrane's resistivity is P ARmen (2nRL)Rmen 2x(2.5 x 10- m)(0.001 m)(2 x 10'S) 7 x 10- m = 4x 10 2 . m b. The total current that passes into the cell through N leak channels is /total = NIchan. Thus, the number of channels is total 3 X 10-9 A N= - ~ = 3 x 104 Ichan 1 x 10-13 A These 30,000 channels are spread out over the surface area A = 2TRL of this segment of the axon, so the surface density of channels is N 3 x 104 channels 2TRL 2x(2.5 x 10- m)(0.001 m) = 2 x 10 2 channels/m~ x 10-6 m 1 um = 2 channels/um