A nerve cell in its resting state has a membrane potential

Chapter 26, Problem 26.105

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A nerve cell in its resting state has a membrane potential of -70 mV, meaning that the potential inside the cell is 70 mV less than the potential outside due to a layer of negative charge on the inner surface of the cell wall and a layer of positive charge on the outer surface. This effectively makes the cell wall a charged capacitor. When the nerve cell fires, sodium ions, Na+, flood through the cell wall to briefly switch the membrane potential to +40 mV. Model the central body of a nerve cellthe somaas a 50-mm-diameter sphere with a 7.0-nm-thick cell wall whose dielectric constant is 9.0. Because a cells diameter is much larger than the wall thickness, it is reasonable to ignore the curvature of the cell and think of it as a parallel-plate capacitor. How many sodium ions enter the cell as it fires?