BIO Axons. Neurons are the basic units of the nervous system They contain long tubular structures called axons that propagate electrical signals away from the ends of the neurons. The axon contains a solution of potassium ions K+ and large negative organic ions. The axon membrane prevents the large ions from leaking out, but the smaller K+ ions are able to penetrate the membrane to some degree. (See Figure 18.35.) This leaves an excess of negative charge on the inner surface of the axon membrane and an excess of positive charge on the outer surface, resulting in a potential difference across the membrane that prevents further K+ ions from leaking out Measurements show that this potential difference is typically about 70 mV. The thickness of the axon membrane itself varies from about 5 to 10 nm, so we’ll use an average of 7.5 nm. We can model the membrane as a large sheet having equal and opposite charge densities on its faces (a) Find the electric field inside the axon membrane, assuming (not too realistically) that it is filled with air. Which way does it point, into or out of the axon? (b) Which is at a higher potential, the inside surface or the outside surface of the axon membrane?
Figure 18.35
Problem 11.
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- 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 2.0 103 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 Figure P18.43. 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 = 1.0 108 m, axon radius r = 1.0 101 m, and cell-wall dielectric constant = 3.0. (a) Calculate the positive charge on the outside of a 0.10-m piece of axon when it is not conducting an electric pulse. How many K+ ions are on the outside of the axon assuming an initial potential difference of 7.0 102 V? Is this a large charge per unit area? Hint: Calculate the charge per unit area in terms of electronic charge e per squared (2). An atom has a cross section of about 1 2 (1 = 1010 m). (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? 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 + 3.0 102 V, starting from the resting potential of 7.0 102 V? Figure P18.43 Problem 43 and 44.arrow_forwardPlease ASAP. Thankyou. Question 20 If the distance between the two sides of the phospholipid bilayer were to increase by 4-fold, what would happen to the capacitance of the membrane? Increase 4-fold Increase 8-fold It would be 1/4 It would be ⅛arrow_forwardAn axon is the relatively long tail-like part of a neuron, or nerve cell. The outer surface of the axon membrane (dielectric constant = 5, thickness = 1 × 10^–8 m) is charged positively, and the inner portion is charged negatively. Thus, the membrane is a kind of capacitor. If the membrane acts like a parallel plate capacitor with a plate area of 5 × 10^–6 m^2, what is its capacitance?arrow_forward
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