Ion Flow Through a Channel: Current and Charge

[GBC]

Sodium ion flows a through a cylindrical ion channel --> diameter = 0.85 um and is 5 um long.
potential difference b/w the ends of the channel is 225 mV
drift velocity = 0.015 m/s
in a period of 1 ms, a total of 15*10^6 ions exit the channel

a. total charge exiting the channel in 1 ms =?
b. current in the ion channel=?
i have been trying to find b.) but I think my values might be wrong... PLEASE HELP ME!

Homework Equations

Q=qnV
I=qnAv=Q/change in time
change in time = length/drift velocity
n=N/Vso for a. using the formula for Q:
q=1.6*10^-19
N=15*10^6
V=l*PIr^2= (5 um)(PI)(4.25*10^-7)^2=2.8*10^-18
plugging in this value to the equation of Q, I get:
Q=2.4*10^-12 (acc to the solutions on the book, this is right)

Now, my problem is b...
in this part, I used I=Q/t
i know t = length/velocity so i plug in giving me =(5 um)(0.015 m/s)
so now that i have t, i just use the Q from a to solve for I and I get 7.2*10^-9.
however, according to the solutions this is wrong. it is suppose to be 2.4*10^-9...
I have a feeling my Q value for this question is wrong since it's asking for the current IN the ion channel and the Q-value i have is the total charge exiting the channel... so how do I find the Q IN the ion channel??
please help me..!

 

[gneill]

You were given the time interval over which the stated number of ions exited the channel. It was 1 ms. That's the timeframe that is important for figuring the current.

The drift velocity and channel dimensions are related to the current density. The time for a given ion to traverse the channel is not so important when there are many, many ions in a cross-section of the channel.

 

[GBC]

Oh Thank you so much! I have never taken physics back in high school so this is all new to me. I was sort of confused on what it meant by "period of 1 ms" (I thought it was a typo for m/s... I have never seen millisecond used before haha) so thank you for explaining it! :)