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 = CΔV to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.1 ✕ 10−8 m, axon radius r = 2.0 ✕ 101 ?m, and cell-wall dielectric constant ? = 2.7. A diagram shows a collection of positive and negative charges in and around an axon. The diagram is divided into three sections, one on top of the other. The top section is labeled "External fluid". A row of positive charges labeled "Positive charge layer" lies along the bottom side of this section. Above the row of positive charges, there is an even mixture of positive and negative charges. The middle section has thickness d and is labeled "Axon wall membrane". There are no charges in this section. The bottom section is labeled "Internal fluid". A row of negative charges labeled "Negative charge layer" lies along the top side of this section. Below the row of negative charges, there is an even mixture of positive and negative charges that is less dense than the mixture of charges in the external fluid. The axon radius r is drawn from a point in the internal fluid's mixture of charges to the center of the axon wall membrane. (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.) C How many K+ ions are on the outside of the axon assuming an initial potential difference of 7.0 ✕ 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 (Å2). 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.) YesNo

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 = CΔV to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.1 ✕ 10−8 m, axon radius r = 2.0 ✕ 101 ?m, and cell-wall dielectric constant ? = 2.7. A diagram shows a collection of positive and negative charges in and around an axon. The diagram is divided into three sections, one on top of the other. The top section is labeled "External fluid". A row of positive charges labeled "Positive charge layer" lies along the bottom side of this section. Above the row of positive charges, there is an even mixture of positive and negative charges. The middle section has thickness d and is labeled "Axon wall membrane". There are no charges in this section. The bottom section is labeled "Internal fluid". A row of negative charges labeled "Negative charge layer" lies along the top side of this section. Below the row of negative charges, there is an even mixture of positive and negative charges that is less dense than the mixture of charges in the external fluid. The axon radius r is drawn from a point in the internal fluid's mixture of charges to the center of the axon wall membrane. (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.) C How many K+ ions are on the outside of the axon assuming an initial potential difference of 7.0 ✕ 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 (Å2). 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.) YesNo

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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Question

A diagram shows a collection of positive and negative charges in and around an axon. The diagram is divided into three sections, one on top of the other.

The top section is labeled "External fluid". A row of positive charges labeled "Positive charge layer" lies along the bottom side of this section. Above the row of positive charges, there is an even mixture of positive and negative charges.

The middle section has thickness d and is labeled "Axon wall membrane". There are no charges in this section.

The bottom section is labeled "Internal fluid". A row of negative charges labeled "Negative charge layer" lies along the top side of this section. Below the row of negative charges, there is an even mixture of positive and negative charges that is less dense than the mixture of charges in the external fluid. The axon radius r is drawn from a point in the internal fluid's mixture of charges to the center of the axon wall membrane.

(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.)
C

How many K⁺ ions are on the outside of the axon assuming an initial potential difference of 7.0 ✕ 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 (Å²). 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.)

YesNo

(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 ✕ 10⁻² 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 ✕ 10⁻² V, starting from the resting potential of −7.0 ✕ 10⁻² V? (Assume that no energy is required to first raise the potential to 0 V from the resting potential of −7.0 ✕ 10⁻² V.)
J

This diagram illustrates the electrochemical structure of an axon, a critical component of nerve cells responsible for conducting electrical impulses.

- **External Fluid:** The top section shows the external environment of the axon, where both positive (+) and negative (-) ions are present. This region is labeled as the "Positive charge layer."

- **Axon Wall Membrane:** A purple band represents the membrane of the axon. The distance of the membrane is marked as "d." This membrane separates the external fluid from the internal fluid of the axon.

- **Internal Fluid:** Below the membrane, the internal fluid of the axon is depicted, containing a balance of positive and negative ions. This region is labeled as the "Negative charge layer."

- **Axon Radius:** The radius of the axon is denoted by "r."

This setup implies that the axon membrane helps create a potential difference by maintaining distinct layers of charge (positive externally and negative internally), essential for the transmission of nerve signals.

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