Answer:
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
A) The number of potassium ions that will pass through the ion channel; 11250
B) The current density in the ion channel = 2.55 × 10⁷ A/m²
Given data;
Measurement with microelectrodes = 0.30-nm- diameter
K⁺ = 1.8 pA
a) calculate the number of potassium ions that passes through the ion channel
given that the channel opens for 1.0 ms
first step ; determine the value of charge ( Q )
Q = I*Δt = ( 1.8 × 10⁻¹² A )*(1.0 × 10⁻³ s ) = 1.8 × 10⁻¹⁵ C
where ; I = 1.8 × 10⁻¹² A
Δt = 1.0 × 10⁻³ s
next step : determine number of K⁺ ions passing through
NK⁺ = Q*e = ( 1.8 × 10⁻¹⁵ C )*( 1.60 × 10⁻¹⁹ C) = 11250
∴ number of K⁺ ions passing through = 11250 ions.
B) determine the current density in the ion channel
current density = current * size of channel
= ( 1.8 * 10⁻¹² ) * ( π * ( 0.30 * 10⁻⁹ )²
= 2.55 × 10⁻⁷ A/m²
Hence we can conclude that the number of potassium ions that will pass through the ion channel; 11250 and The current density in the ion channel = 2.55 × 10⁷ A/m²
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