What is the current density in the ion channel?

[kyang002]

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?

I am completely lost for this one. Anyone know of any equations that I can use?

 

[K.J.Healey]

Some helpful steps :
Remember what current is, its I = dQ/dt, the flow of charge through a point, through time. Like measuring the flow of water through a pipe.
Simple calculus, or just realizing what it means can give you the equaiton
You know the area the flow is going through (the inner area of the "pipe") because they give you the diameter. area = pi*r^2, 2*r = diameter.
The CHARGE that's flowing through with each ion is what? Do you understand what it is? Its a K+ ion, so you need to understand what charge it is carrying (in terms of electron charge). Its quite simple.
I think you had a similar equation to what you need now.
I = dQ/dt = n*A*q*dx/dt = n*A*q*Velocity
so first solve I = n*A*q*Velocity
then use that with velocity = dx/dt to get dx.
Then use dQ = (n*A*dx)*q
to get dQ.
Thats a start. I think its right, I can be wrong.

 

[wais]

The current density in the ion channel can be calculated using the equation J = I/A, where J is the current density, I is the current, and A is the cross-sectional area of the channel. In this case, the current is 1.8 pA and the cross-sectional area can be calculated using the formula A = πr^2, where r is the radius of the channel (0.30 nm/2 = 0.15 nm). Therefore, the cross-sectional area is approximately 0.0707 nm^2. Plugging in these values, the current density is approximately 25.5 pA/nm^2.

To calculate the number of potassium ions that pass through the channel in 1.0 ms, we can use the equation Q = I*t, where Q is the charge, I is the current, and t is the time. In this case, the charge is equal to the number of ions multiplied by the charge of each ion (1.8 pA * 1.0 ms = 1.8 x 10^-6 C). The charge of a potassium ion is approximately 1.6 x 10^-19 C. Therefore, the number of potassium ions that pass through the channel in 1.0 ms is approximately 1.1 x 10^13 ions.

In summary, the current density in the ion channel is approximately 25.5 pA/nm^2 and the number of potassium ions that pass through in 1.0 ms is approximately 1.1 x 10^13 ions.