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BIO Transmission of Nerve Impulses. Nerve cells transmit electric signals through their long tubular axons. These signals propagate due to a sudden rush of \(\mathrm{Na}^{+}\) ions, each with charge \(+e,\) into the axon. Measurements have revealed that typically about \(5.6 \times 10^{11} \mathrm{Na}^{+}\) ions enter each meter of the axon during a time of \(10 \mathrm{~ms}\). What is the current during this inflow of charge in a meter of axon?

Short Answer

Expert verified
The current during the inflow of charge in a meter of axon can be found by performing the calculations listed in the step-by-step solution.

Step by step solution

01

Determine the total charge transferred

Calculate the total amount of electric charge transferred into the axon using the formula for charge: \(Q = n \times e\), where \(n\) is the number of ions and \(e\) represents the charge of each ion. Given that \(n = 5.6 \times 10^{11}\) ions and \(e\) is the elementary charge \(e = 1.6 \times 10^{-19} C\), where \(C\) represents coulombs, we find \(Q = 5.6 \times 10^{11} \times 1.6 \times 10^{-19} C\).
02

Compute the electric current

Now that we know the total charge transferred, the electric current, \(I\), can be found by dividing this by the time interval of the transfer. Given a time of \(10 ms = 10 \times 10^{-3} s\), we can use the formula for electric current: \(I = Q / t\). Substituting the values from step 1 gives \(I = Q / 10 \times 10^{-3} s\).
03

Calculate the numerical value

Carrying out the arithmetic from the previous steps will give us the final numerical answer, which represents the electric current in the given axon during the inflow of charge.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electric Current
Electric current is the flow of electric charge. In the context of nerve impulses, it is essential for transmitting signals through nerve cells. When sodium ions (Nova^{+}) rush into an axon, they carry positive charge with them. This movement of charge over time creates an electric current.

To calculate the electric current, you must know the total charge transferred and the duration of the transfer. The formula to find electric current (I) is \(I = \frac{Q}{t}\), where \(Q\) is the electric charge in coulombs, and \(t\) is the time in seconds. This formula helps us determine how rapidly charge flows through a meter of the axon.

Electric current is vital for nerve signal transmission, influencing how quickly and effectively a nerve message travels.
Axon
The axon is a long, tubular structure in a nerve cell responsible for conducting electrical impulses. Each neuron typically has one axon, which can be very short or extend up to a meter in length, depending on the organism and the type of neuron.

Axons are crucial for sending signals from one part of the nervous system to another, which might mean sending instructions to move a muscle or signaling pain to the brain. This is where the sodium ions enter, allowing the axon to depolarize and propagate the signal forward.

In essence, the axon is like a highway for electric signals, facilitated by ion movements, ensuring swift communication within the body.
Elementary Charge
The elementary charge, denoted by \(e\), is the smallest unit of electric charge that exists independently. It has a value of approximately \(1.6 \times 10^{-19} \ \mathrm{C}\) (coulombs). This value is fundamental in calculating the electric charge that ions, such as sodium ions (Nova^{+}), carry.

Understanding elementary charge is pivotal in calculating the total charge transferred when ions move. For instance, with \(n\) sodium ions, each having \(e\), the total charge (Q) entering the axon can be expressed by the equation \(Q = n \times e\).

This concept helps connect the microscopic world of ions with the macroscopic electrical phenomena we can measure, such as nerve impulses.
Sodium Ions
Sodium ions, represented as Nova^{+} , play a pivotal role in nerve impulse transmission. They are positively charged ions that move across the cell membrane of the axon during a nerve impulse, changing the electric potential of the neuron.

The rush of sodium ions into the axon is a key part of the action potential process, which is how neurons send signals. This ion movement into the axon causes depolarization, the first step in the chain reaction that results in an electrical impulse traveling down the axon.

Without sodium ions, nerve impulses as we know them would not occur. They are essential for the rapid and precise transmission of signals that control everything from simple reflexes to complex thoughts.

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Most popular questions from this chapter

A metal wire has a circular cross section with radius \(0.800 \mathrm{~mm}\) You measure the resistivity of the wire in the following way: You connect one end of the wire to one terminal of a battery that has emf \(12.0 \mathrm{~V}\) and negligible internal resistance. To the other terminal of the battery you connect a point along the wire so that the length of wire between the battery terminals is \(d\). You measure the current in the wire as a function of \(d\). The currents are small, so the temperature change of the wire is very small. You plot your results as \(I\) versus \(1 / d\) and find that the data lie close to a straight line that has slope \(600 \mathrm{~A} \cdot \mathrm{m} .\) What is the resistivity of the material of which the wire is made?

\(\mathrm{A} \cdot 540 \mathrm{~W} "\) electric heater is designed to operate from \(120 \mathrm{~V}\) lines. (a) What is its operating resistance? (b) What current does it draw? (c) If the line voltage drops to \(110 \mathrm{~V}\), what power does the heater take? (Assume that the resistance is constant. Actually, it will change because of the change in temperature.) (d) The heater coils are metallic, so that the resistance of the heater decreases with decreasing temperature. If the change of resistance with temperature is taken into account, will the electrical power consumed by the heater be larger or smaller than what you calculated in part (c)? Explain.

A dielectric of permittivity \(3.5 \times 10^{-11} \mathrm{~F} / \mathrm{m}\) completely fills the volume between two capacitor plates. For \(t>0\) the electric flux through the dielectric is \(\left(8.0 \times 10^{3} \mathrm{~V} \cdot \mathrm{m} / \mathrm{s}^{3}\right) t^{3} .\) The dielectric is ideal and nonmagnetic; the conduction current in the dielectric is zero. At what time does the displacement current in the dielectric equal \(21 \mu \mathrm{A} ?\)

A ductile metal wire has resistance \(R\). What will be the resistance of this wire in terms of \(R\) if it is stretched to three times its original length, assuming that the density and resistivity of the material do not change when the wire is stretched? (Hint: The amount of metal does not change, so stretching out the wire will affect its cross-sectional area.)

The armature of a small generator consists of a flat, square coil with 120 turns and sides with a length of \(1.60 \mathrm{~cm} .\) The coil rotates in a magnetic field of \(0.0750 \mathrm{~T}\). What is the angular speed of the coil if the maximum emf produced is \(24.0 \mathrm{mV} ?\)

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