General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
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Chapter 18, Problem 17E
To determine
The equilibrium potential at
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Assume an axon has the same characteristics as the class example
except the radius of the axon is 0.005 mm and the membrane
thickness is 20.0 nm. The percentage fractional change in the
concentration of Na+ ions in the axon during one action potential is
%? Record the answer to the nearest one
thousandth.
Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed x pulse duration
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 = K² A/d and Q
radius r = 1.6 × 10¹ μm, and cell-wall dielectric constant x = 2.9.
=
Positive
charge
layer
Negative
charge
layer
+
External fluid
Axon wall membrane
No
Axon radius = r
+
Internal fluid
+
How many sodium ions (Na+) is this?
Na+ ions
d
+
(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.)
-2
9.03E-10
C
How many K+ ions are on the outside of the axon assuming an initial potential difference of 7.0 × 10-² V?
5.639E9
K+ ions
= 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
CAV to investigate the…
Assume the axon had a diameter of 30 um and was 5 cm long. The
capacitance of this axon would be
Chapter 18 Solutions
General Physics, 2nd Edition
Ch. 18 - Prob. 1RQCh. 18 - Prob. 2RQCh. 18 - Prob. 3RQCh. 18 - Prob. 4RQCh. 18 - Prob. 5RQCh. 18 - Prob. 6RQCh. 18 - Prob. 7RQCh. 18 - Prob. 8RQCh. 18 - Prob. 9RQCh. 18 - Prob. 10RQ
Ch. 18 - Prob. 1ECh. 18 - Prob. 2ECh. 18 - Prob. 3ECh. 18 - Prob. 4ECh. 18 - Prob. 5ECh. 18 - Prob. 6ECh. 18 - Prob. 7ECh. 18 - Prob. 8ECh. 18 - Prob. 9ECh. 18 - Prob. 10ECh. 18 - Prob. 11ECh. 18 - Prob. 12ECh. 18 - Prob. 13ECh. 18 - Prob. 14ECh. 18 - Prob. 15ECh. 18 - Prob. 16ECh. 18 - Prob. 17ECh. 18 - Prob. 18ECh. 18 - Prob. 20ECh. 18 - Prob. 21ECh. 18 - Prob. 24ECh. 18 - Prob. 25ECh. 18 - Prob. 26E
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- 12. (a) Using Eq. AQ=CAV and the data in the Table, calculate the number of ions entering the axon during the action potential, per meter of nonmyelinated axon length. (The charge on the ion is 1.6 x 10-19 coulomb.) (b) During the resting state of the axon, typical concentrations of sodium and potassium ions inside the axon are 15 and 150 millimole/liter, respectively. From the data in the Table, calculate the number of ions per meter length of the axon. Table 13.1 Properties of Sample Axons Hint: 1 F (farad) = 1coulomb/1 volt Property Nonmyelinated axon Myelinated axon Axon radius 5 x 10-m 5 x 10-6 m 1 mole /liter = 6.02 x 1020 particles (ions, atoms, etc. ) Resistance per unit length of fluid cm 6.37 x 10°2/m 6.37 x 10°2/m both inside and outside axon (r) Conductivity per unit length of axon membrane (gm) 1.25 x 10-4 mho/m In the resting state, the axon voltage is -70mV. During the pulse, the voltage changes to about +30mV, resulting in a net voltage change across the membrane of 100…arrow_forwardA single ion channel is selectively permeable to K+ and has a resistance of 2.20 G-ohm. During an experiment, the channel is open for approximately 1.15 ms while the voltage across the channel is maintained at +85.5 mV with a patch clamp. How many ions, N, travel through the channel?arrow_forwardThe velocity of spike propagation is proportional to the following combination of factors: 1 a C, V R„R, m Where a is the radius of the axon, Rm and R; are specific resistances of the membrane and the internal buffer, respectively. If we double the radius and simultaneously increase the concentration of salt inside the axon twice (i.e. R; decreases two times), by how many fold will the velocity change?arrow_forward
- In a typical mammalian cell, the net transport by the sodiumpotassium exchange pump that maintains the 70 mV membrane potential is 500 singly charged ions per second. How much work does the pump do each second?arrow_forwarda) What was the smallest voltage required to produce a contraction (the threshold voltage)? What proportion of the fibers in the muscle do you think were contracting to produce this small response? b) What was the smallest voltage required to produce the maximum (largest) contraction? What proportion of the fibers in the muscle do you think were contracting to produce this maximal response?arrow_forwardSuppose that you apply an external voltage (from a battery) to a pn junction where the n-doped part is connected to the positive terminal of the battery while the p-side is connected to the negative terminal of the battery.(a) What happens to the depletion region and why?(b) What happens to the internal electric field?(c) What happens to the current across the junction?arrow_forward
- Find the radius of the unmyelinated axon (m) with space parameter A = 14 mm, (Resistance of a unit area of the membrane, Rm =0.2 Q.m², Resistivity of axoplasm, p, =2 Q.m). A. 0.00392 B. 0.01568 C. None D. 0.02352 E. 0.00784arrow_forwardNerve cells in your body can be electrically stimulated; a large enough change in a membrane potential triggers a nerve impulse. Certain plants work the same way. A touch to mimosa pudica, the “sensitive plant,” causes the leaflets to fold inward and droop. We can trigger this response electrically as well. In one experiment, investigators placed electrodes on the thick tissue at the base of a leaf. The electrodes were 3.5 mm apart. When the electrodes were connected to a 47 μF capacitor charged to 1.5 V, this stimulated a response from the plant.a. Eventually, all the charge on the capacitor was transferred to the plant. How much charge was transferred?b. What was the approximate electric field between the electrodes?arrow_forwardIf the distance between the two sides of the phospholipid bilayer were to increase by 4-fold, what would happen to the capacitance of the membrane? Increase 4-fold Increase 8-fold It would be 1/4 It would be 1/8arrow_forward
- Please help. The nonpolar core of the membrane of a muscle cell has a thickness d = 4nm and a dielectric constancy k = 20. (a) What is the surface capacity of the membrane? Express your response in microcoulombs per square centimeter. (b) During muscle contraction, the internal potential of the cell increases by about 100 mV. For 1 cm2 of membrane, how many Na+ ions must have entered the cell for this purpose? (c) The medium outside the cell initially contains 0.150 mol / L of Na + ions in solution. Considering that it extends to 1 µm from the cell, what is the decrease in Na+ concentration immediately after the change in potential? (d) Estimate the number of times the process can be repeated before the Na+ ion reserve is exhausted. Please show formulas ans steps for my own understandingarrow_forwardFind the radius of the unmyelinated axon (m) with space parameter A = 11 mm, (Resistance of a unit area of the membrane, R =0.2 Q.m?, Resistivity of axoplasm, p. =2 0.m). A. 0.00968 B. 0.00242 C. 0.00484 D. None E. 0.01452arrow_forwardCalculate the axoplasm resistance for a neuron of length 0.06 m and a radius of 5 um. The axoplasm resistivity is 2.0 Ohm.m. Give your answer in MOhmsarrow_forward
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