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Chapter 4: Q86PP (page 880)

Assume that a typical open ion channel spanning an axon’s membrane has a resistance of 1 * 1011 Ω. We can model this ion channel, with its pore, as a 12-nm-long cylinder of radius 0.3 nm. What is the resistivity of the fluid in the pore? (a) 10 Ω.m; (b) 6 Ω.m; (c) 2 Ω.m; (d) 1 Ω.m

Short Answer

Expert verified

The resistivity is2.4Ω/nm

Step by step solution

01

Resistivity of conductor.

Consider a typical open ion channel spanning an axon’s membrane which has a resistance of R = 1×1011Ω.The model of this ion channel with its pore can be treated as a l = 12nm long cylinder of radius r = 0.3nm. The resistance of a cylinder shape conductor is given by,

R=ρlA

Where A =πr2 is the cross-sectional area andis the resistivity. Thus,

ρ=ARl=πr2Rl

Substitute with the given we get,

ρ=π0.3nm21×1011Ω12nm=2.4×109Ω/nm=2.4Ω/nmρ=2.4Ω/nm

02

Result

Hence, the resistivity is2.4Ω/nm

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