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Neurons are components of the nervous system of the body that transmit signals as electrical impulses travel along their length. These impulses propagate when charge suddenly rushes into and then out of a part of the neuron called an axon. Measurements have shown that, during the inflow part of this cycle, approximately \(5.6 \times 10^{11} \mathrm{Na}^{+}\) (sodium ions) per meter, each with charge \(+e,\) enter the axon. How many coulombs of charge enter a \(1.5 \mathrm{~cm}\) length of the axon during this process?

Short Answer

Expert verified
The total inflow of charge into a 1.5 cm length of the axon during this process is approximately \(1.34 \times 10^{-9}\) coulombs.

Step by step solution

01

Convert centimeters to meters

Before proceeding, make sure all measurements are in compatible units. The length of the axon is given in centimeters, but the number of sodium ions is provided per meter. So, convert the length from centimeters to meters first. As 1 meter = 100 centimeters, 1.5 centimeters = 1.5 / 100 = 0.015 meters.
02

Calculate the total number of sodium ions

Multiply the given number of sodium ions per meter by the length of the axon in meters to find the total number of ions. This means \(5.6 \times 10^{11} \mathrm{Na+}\, ions/m \times 0.015 m = 8.4 \times 10^{9} \mathrm{Na+}\, ions.\
03

Calculate total charge

The total charge in coulombs is calculated by multiplying the total number of sodium ions by the charge of a single ion. As mentioned, the charge of an individual sodium ion is \(+e\), which equals \(1.6 \times 10^{-19}\) coulombs. Therefore, the total charge would be \((8.4 \times 10^{9}) ions \times (1.6 \times 10^{-19} C/ion) = 1.34 \times 10^{-9} C.\) The ions are positively charged so the overall charge will also be positive.

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Key Concepts

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

Understanding Neurons
Neurons are specialized cells that are the building blocks of the nervous system. They play a critical role in transmitting information throughout the body. These cells communicate with each other through electrical and chemical signals. The process of sending signals involves the movement of electric charges along the neuron.
Neurons consist of several parts, including dendrites, a cell body, and an axon. Each of these plays a vital role in the functioning of neurons, but the axon is particularly important in transmitting electrical impulses away from the neuron's cell body.
The transmission of these signals happens rapidly, allowing neurons to send messages over long distances in the body. This capability is essential for coordinating activities such as movement, perception, and thought processes.
Key points about neurons:
  • They are the main cells of the nervous system.
  • They transmit information using electrical impulses.
  • Their structure includes dendrites, a cell body, and an axon.
The Role of the Axon
The axon is a vital component of the neuron. It is a long, slender structure that extends from the neuron's cell body and can be several meters long in some cases. Axons are responsible for transmitting electrical impulses away from the neuron's cell body to other neurons, muscles, or glands.
The axon's main job is to ensure that the signal reaches its intended target quickly and efficiently. This is vital for the functioning of the nervous system, as delays in signal transmission could lead to miscommunication between cells.
During transmission, ions enter and exit the axon through channels in its membrane. This movement of ions is what generates the electrical impulses. The rapid influx and efflux of ions are essential for the propagation of nerve impulses along the axon.
Important aspects of axons include:
  • They carry electrical signals away from the cell body.
  • They have specific channels for ion movement.
  • They ensure rapid and accurate signal transmission.
Electric Charge in Neurons
Electric charge is a key element in the neuron's ability to send signals. In the context of neurons, ions are the charged particles that facilitate these signals. The movement of ions across the neuron's membrane creates an electrical current.
Each type of ion has a specific charge; for instance, sodium ions (\(\text{Na}^+\)) have a positive charge. This charge plays an integral role in creating the potential difference across the neuron's membrane, which is necessary for the initiation of nerve impulses.
When a neuron is activated, a rapid movement of ions occurs, creating an electrical impulse that travels along the axon. This impulse is what allows for communication between neurons and other cells in the body.
Key concepts of electric charge in neurons include:
  • Ions are charged particles essential for signal transmission.
  • Sodium ions are positively charged.
  • The movement of ions generates an electrical current.
Understanding Coulombs
The coulomb is the standard unit of electric charge in the International System of Units (SI). It is used to quantify the amount of electric charge. In the case of neurons, understanding coulombs helps us measure how much charge is being transferred during the signal transmission process.
One coulomb is equivalent to the charge of approximately \(6.242 \times 10^{18}\) electrons. In typical neural activity, the charges involved are much smaller, usually measured in nanocoulombs or picocoulombs.
In the context of the original problem, we calculated the total charge transferred as sodium ions entered a length of axon. By multiplying the number of sodium ions by their charge (each is \(+1.6 \times 10^{-19}\) coulombs), we found the total charge involved was \(1.34 \times 10^{-9}\) coulombs.
Essential points about coulombs:
  • It is the unit of electric charge.
  • Used to measure charges in neurons.
  • Helps quantify electricity flowing through neurons.

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