Question

The biochemistry that takes place inside cells depends on various elements, such as sodium, potassium, and calcium, that are dissolved in water as ions. These ions enter cells through narrow pores in the cell membrane known as ion channels. Each ion channel, which is formed from a specialized protein molecule, is selective for one type of ion. High-resolution measurements have shown that an ion channel is a 0.30-nm-diameter cylinder with length of 5.0 nm. The intracellular fluid filling the ion channel has resistivity 0.60 Ω⋅m.

What is the resistance of the ion channel?

Express your answer in ohms.

Answer 1

Resistance is given by:

R = rho*L/A

rho = resistivity of intracellular fluid = 0.60 ohm-m

L = length of ion channel = 5.0 nm = 5.0*10^-9 m

A = Cross-sectional Area of cylinder = pi*d^2/4

d = diameter = 0.30 nm = 0.30*10^-9 m

A = pi*(0.30*10^-9)^2/4 = 7.068*10^-20 m^2

So,

R = 0.60*5.0*10^-9/(7.068*10^-20)

R = 4.24*10^10 ohm = resistance of ion channel

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