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. measurements with microelectrodes have shown that a 0.30-nm-diameter potassium ion (k+) channel carries a current of 1.8 pa. how many potassium ions pass through if the ion channel opens for 1.0 ms? what is the current density in the ion channel?

Explanation:

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. Measurements with microelectrodes have shown that a 0.30-nm-diameter potassium ion (K+) channel carries a current of 1.8 pA.

Part A. How many potassium ions pass through if the ion channel opens for 1.0 ms?

Part B. What is the current density in the ion channel?

Solution: In 1.0 ms, the charge that passes through is

Q = I ∆t =

( 1.8 × 10−12 A ) (1.0 × 10−3 s )

= 1.8 × 10−15 C

Since each ion has a +1 charge (measured in electron charges), this represents

NK+ = Q e = (1.8 × 10−15 C ) (1.60 × 10−19 C) = 11250

The current density is calculated from the current and the size of the channel.

J = I A = ( 1.8 × 10−12 A ) ( π (0.30 × 10−9 m/2)2 ) = 2.55 × 107 A/m2

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