Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Textbook Question
Chapter 25, Problem 60P
(I) What is the magnitude of the electric field across an axon membrane 1.0 × 10-8 m thick if the resting potential is −70 mV?
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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?
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…
capacitor and take C = xe A/d and Q = CAV to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.6 x 10-8 m, axon radius r = 2.0 x 10¹ μm, and
cell-wall dielectric constant x = 2.2.
Positive
charge
layer
Negative {
charge
layer
External fluid
Axon wall membrane
1
O No
O
Internal fluid
Axon radius = r
+
d
Q
(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 x 10-2 v.)
C
How many K+ ions are on the outside of the axon assuming an initial potential difference of 7.0 x 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 (A2). An atom has a cross section of about 1 A²
(1 A = 10-10 m). (Compare to normal atomic spacing of one atom every few A.)
Yes
Chapter 25 Solutions
Physics for Scientists and Engineers with Modern Physics
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