Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed pulse duration = 50.0 m/s 0.0020 s = 0.10 m). 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 the figure below. Model the axon as a parallel-plate capacitor and take C = ₀A/d and Q = CV to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.8 10⁸ m, axon radius r = 2.0 10¹ m, and cell-wall dielectric constant = 2.5.

a) Calculate the positive charge on the outside of a 0.10-m piece of axon when it is not conducting an electric pulse. (Assume an initial potential difference of 7.0 10² V.) . C How many K⁺ ions are on the outside of the axon assuming an initial potential difference of 7.0 10² V? . K⁺ ions

b) How much positive charge must flow through the cell membrane to reach the excited state of +3.0 10² V from the resting state of 7.0 10² V? . C How many sodium ions (Na⁺) is this? . Na⁺ ions

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? . A d) How much energy does it take to raise the potential of the inner axon wall to +3.0 10² V, starting from the resting potential of 7.0 10² V? (Assume that no energy is required to first raise the potential to 0 V from the resting potential of 7.0 10² V.) . J