Action Potential with Nerve Cell and Finding Power

In summary, to produce a flow of Na+ ions into the cell at a rate of 3 x 10^-7 mol/m^2 s against a +30 mV potential difference, the "active Na+ pumping" system must produce approximately 9.09 x 10^-9 watts of power. This can be calculated using the formula P=IV and taking into account the dimensions of the axon and the unit charge of an Na+ ion. The resistivity of the liquid is also needed but can be assumed to be water.
  • #1
PeachBanana
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Homework Statement



During an action potential, Na + ions move into the cell at a rate of about 3 x 10^-7 mol / m^2 s. How much power must be produced by the "active Na+ pumping" system to produce this flow against a + 30 mv potential difference? Assume that the axon is 40cm long and 30 mu m in diameter.

Homework Equations



P = IV
maybe R = ρL / A

The Attempt at a Solution



I understand I need to use P=IV but I don't understand how to incorporate the measurements of the axon without knowing the resistivity of the liquid. Should I assume water?

P = (3.7 * 10^-7 mol/m^2 s)(0.03 V)
P ≈ 9.09 * 10^-9 W
 
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  • #2
The diffusion rate is given in terms of moles per unit area per second. Use the axon dimensions to estimate area. You'll also have to convert the moles of charges into actual charge units (what's the unit charge of an Na+ ion in coulombs?).
 

1. What is an action potential?

An action potential is a brief electrical signal that travels along the membrane of a nerve cell, also known as a neuron. It is a key component in the communication between neurons, allowing for the transmission of information throughout the nervous system.

2. How does a nerve cell generate an action potential?

A nerve cell generates an action potential through a series of changes in the electrical charge of its membrane. This is accomplished by the movement of ions, such as sodium and potassium, across the cell membrane through specialized channels.

3. What is the role of ion channels in generating an action potential?

Ion channels are specific proteins found in the cell membrane that allow for the movement of ions in and out of the cell. In the case of generating an action potential, ion channels open and close in response to changes in the electrical charge of the membrane, allowing for the movement of ions and the propagation of the electrical signal.

4. How is the power of an action potential measured?

The power of an action potential is typically measured in millivolts (mV), which represents the difference in electrical charge between the inside and outside of the cell membrane. The peak power of an action potential can range from 40-100 mV, depending on the type of neuron and its location in the nervous system.

5. What are some factors that can affect the power of an action potential?

The power of an action potential can be influenced by various factors, such as the concentration of ions inside and outside the cell, the thickness of the cell membrane, and the presence of certain drugs or toxins. Additionally, the frequency and timing of action potentials can also impact their overall power and effectiveness in transmitting information between neurons.

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