Assume that a length of axon membrane of about 10 cm is excited by an action potential (length excited = nerve speed pulse duration = 50 m/s 2.0 ms ? 10 cm). In the resting state, the outer surface of the axon wall is charged positively with K⁺ ions and the inner wall has an equal and opposite charge of negative organic ions, as shown in Figure. Model the axon as a parallel-plate capacitor, and take C = ??₀A/d and Q = C?V to investigate the charge as follows: Use typical values for a cylindrical axon of cell wall thickness d = 1.0 x 10^?8 m, axon radius r = 10 ?m, and cell-wall dielectric constant ? = 3.0.

(a) Calculate the positive charge on the outside of a 10-cm piece of axon when it is not conducting an electric pulse. How many K⁺ ions are on the outside of the axon? Is this a

large charge per unit area?

(b) How much positive charge must flow through the cell membrane to reach the excited state of + 30 mV from the resting state of ? 70 mV? How many sodium ions (Na⁺) is this?

(c) If it takes 2.0 ms for the Na^+?ions to enter the axon, what is the average current in the axon wall in this process?

(d) How much energy does it take to raise the potential of the inner axon wall to + 30 mV, starting from the resting potential of ?70 mV?

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External fluid Positive +, charge layer d = 1.0 x 10m Axon wall membrane Negative charge layer Internal fluid Axon radius = 1.0 x 10-m +. +. +.