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need help on b and c.

need help on b and c.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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need help on b and c.

Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed x pulse duration = 50.0 m/s x 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 = KE A/d and Q = CAV to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.3 x 10-8 m, axon radius r = 1.3 x 10¹ μm, and cell-wall dielectric constant x = 2.1. Positive charge layer Negative charge layer External fluid + + Axon wall membrane Internal fluid Axon radius = r + + + (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 × 10-² V.) 8.10E-10 C How many K+ ions are on the outside of the axon assuming an initial potential difference of 7.0 x 10-² V? 5.11E9 ✔ K+ ions Is this a large charge per unit area? Hint: Calculate the charge per unit area in terms of electronic charge e per angstrom squared (Ų). An atom has a cross section of about 1 Ų (1 Å = 10-10 m). (Compare to normal atomic spacing of one atom every few Å.) O Yes O No (b) How much positive charge must flow through the cell membrane to reach the excited state of +3.0 x 10-2 V from the resting state of -7.0 x 10-² V? 4.67E-10 Your response differs from the correct answer by more than 10%. Double check your calculations. C How many sodium ions (Na+) is this? 2.92E9 X Your response differs from the correct answer by more than 10%. Double check your calculations. Na+ ions + (c) If it takes 2.0 ms for the Nations to enter the axon, what is the average current in the axon wall in this process? 0.233 X Your response differs from the correct answer by more than 10%. Double check your calculations. μА (d) How much energy does it take to raise the potential of the inner axon wall to +3.0 x 10-2 V, starting from the resting potential of -7.0 x 10-2 V? (Assume that no energy is required to first raise the potential to 0 V from the resting potential of -7.0 x 10-² V.) 5.26E-12 J
Transcribed Image Text:Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed x pulse duration = 50.0 m/s x 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 = KE A/d and Q = CAV to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.3 x 10-8 m, axon radius r = 1.3 x 10¹ μm, and cell-wall dielectric constant x = 2.1. Positive charge layer Negative charge layer External fluid + + Axon wall membrane Internal fluid Axon radius = r + + + (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 × 10-² V.) 8.10E-10 C How many K+ ions are on the outside of the axon assuming an initial potential difference of 7.0 x 10-² V? 5.11E9 ✔ K+ ions Is this a large charge per unit area? Hint: Calculate the charge per unit area in terms of electronic charge e per angstrom squared (Ų). An atom has a cross section of about 1 Ų (1 Å = 10-10 m). (Compare to normal atomic spacing of one atom every few Å.) O Yes O No (b) How much positive charge must flow through the cell membrane to reach the excited state of +3.0 x 10-2 V from the resting state of -7.0 x 10-² V? 4.67E-10 Your response differs from the correct answer by more than 10%. Double check your calculations. C How many sodium ions (Na+) is this? 2.92E9 X Your response differs from the correct answer by more than 10%. Double check your calculations. Na+ ions + (c) If it takes 2.0 ms for the Nations to enter the axon, what is the average current in the axon wall in this process? 0.233 X Your response differs from the correct answer by more than 10%. Double check your calculations. μА (d) How much energy does it take to raise the potential of the inner axon wall to +3.0 x 10-2 V, starting from the resting potential of -7.0 x 10-2 V? (Assume that no energy is required to first raise the potential to 0 V from the resting potential of -7.0 x 10-² V.) 5.26E-12 J
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