In Example 23.14 we estimated the capacitance of the cell membrane to be \(89 \mathrm{pF}\), and in Example 23.15 we found that approximately \(10,000 \mathrm{Na}^{+}\)ions flow through an ion channel when it opens. Based on this information and what you learned in this chapter about the action potential, estimate the total number of sodium ion channels in the membrane of a nerve cell.

Example 23.14

Example 23.13

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What is the capacitance of the membrane of the spherical cell specified in Example 23.13? The dielectric constant of a cell membrane is approximately 9.0. PREPARE If we imagine opening up a cell membrane and flatten- ing it out, we would get something that looks like a parallel-plate capacitor with the plates separated by a dielectric as illustrated in FIGURE 23.45. The relevant dimensions are the same as those in Example 23.13.