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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 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 = 1.6 x 10-8 m, axon radius r = 1.7 x 101 um, and cell-wall dielectric constant K = 2.3. External fluid Positive charge layer { Axon wall membrane d Negative charge layer Internal fluid + Axon radius = r

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 = 1.6 x 10-8 m, axon radius r = 1.7 x 101 um, and cell-wall dielectric constant K = 2.3. External fluid Positive charge layer { Axon wall membrane d Negative charge layer Internal fluid + Axon radius = r

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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(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 -2 of 7.0 x 10 v.) C How many K* ions are on the outside of the axon assuming an initial potential difference of 7.0 x 10-2 v? 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 (Å<). An atom has a cross section of about 1 Å2 (1 Å = 10-10 m). (Compare to normal atomic spacing of one atom every few Å.) Yes No (b) How much positive charge must flow through the cell membrane to reach the excited state of +3.0 × 10¬2 V from the resting state of –7.0 x 10-2 v? How many sodium ions (Na+) is this? Nat ions (c) If it takes 2.0 ms for the NaT ions to enter the axon, what is the average current in the axon wall in this process? µA -2 (d) How much energy does it take to raise the potential of the inner axon wall to +3.0 x 10 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.)
Transcribed Image Text:(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 -2 of 7.0 x 10 v.) C How many K* ions are on the outside of the axon assuming an initial potential difference of 7.0 x 10-2 v? 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 (Å<). An atom has a cross section of about 1 Å2 (1 Å = 10-10 m). (Compare to normal atomic spacing of one atom every few Å.) Yes No (b) How much positive charge must flow through the cell membrane to reach the excited state of +3.0 × 10¬2 V from the resting state of –7.0 x 10-2 v? How many sodium ions (Na+) is this? Nat ions (c) If it takes 2.0 ms for the NaT ions to enter the axon, what is the average current in the axon wall in this process? µA -2 (d) How much energy does it take to raise the potential of the inner axon wall to +3.0 x 10 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.)
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 = 1.6 x 10 -8 m, axon radius r = 1.7 x 10- um, and cell-wall dielectric constant K = 2.3. External fluid Positive charge layer + Axon wall membrane d Negative { charge layer Internal fluid Axon radius =r
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 = 1.6 x 10 -8 m, axon radius r = 1.7 x 10- um, and cell-wall dielectric constant K = 2.3. External fluid Positive charge layer + Axon wall membrane d Negative { charge layer Internal fluid Axon radius =r
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