BIO Assume a length of axon membrane of about 0.10 m is excited by an action pot
ID: 2029517 • Letter: B
Question
BIO Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed × pulse duration = 50.0 m/s 2.0 × 10-3 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 has an equal and opposite charge of negative organic ions, as shown in Figure. External fluid Positive charge layer Axon wall memurane d= 1.0 10-8 m Model the axon as a parallel-plate capacitor andNegative {le e e take C = KEoA/d and Q-CLVto investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.0 × 10-8 m, axon radius r = 1.0 × 101 m, and cell-wall dielectric constant K = 3.0. Calculate the charge per unit area in terms of elec- tronic charge e per angstrom squared (A2), assuming an initial potential difference of 7.0 × 10-2 V and axon is not conducting an electric pulse. An atom has a cross section of about 1 A2 (1 A = 10-10 m). charge Tayer Internal fluid -Axon radius-1.0 × lo-s m A. 7.5 x 10 B. 8.6 x 10 o C. 9.7 x 10 D. 6.4 x 106Explanation / Answer
a) The area of each surface of this axom membrane is
A = L (2 pi r) = 0.1 * (2pi * 1* 101 * 10-6) = 6.283 * 10-5 m2
C = K eoA / d = 3 * (8.85 * 10-12) * (6.283 * 10-5) / (1 * 10-8)
C = 1.668 * 10-8 F
In resting state ,the charge on the outer surface of the membrane is Qi = C Vi
= 1.668 * 10-8 * 7 * 10-2
Qi = 1.16 * 10-10 C
N(K) = Qi / e = 1.16 * 10-10 / (1.6 * 10-19)
= 7.29 * 109 K+ ions
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