Solve Electron Current in 1.00mm Gold Wire: How Long for 1 Mole?

[fsm]

Homework Statement

The electron drift speed in a 1.00 -mm-diameter gold wire is 5.50*10^-5 m/s
How long does it take 1 mole of electrons to flow through a cross section of the wire in a day?

Homework Equations

i=n*A*v_d
N_e=i*delta(t)

The Attempt at a Solution

First I figured out the electron current.

i=((5.9*10^28)*(.0005^2*pi)*(5.50*10^-5)
i=2.55*10^18 e-/sec

Since electron current is the amount of electrons per second I multiplied by 86,400s in a day:

N_e=(2.55*10^18)*(86400)
N_e=2.20*10^23

This gives me the number of electrons that pass through a cross sectional area. Since they are asking for 1 mole I divided by 6.02*10^23

(2.20*10^23)/(6.02*10^23)
=.366 days

This answer is wrong. I don't know what I'm doing wrong. Any help?

 

[marcusl]

The electron drift speed in a 1.00 -mm-diameter gold wire is 5.50*10^-5 m/s
How long does it take 1 mole of electrons to flow through a cross section of the wire in a day?

Is there additional information available? Are you sure you copied the problem correctly? The last sentence doesn't make sense.

 

[hage567]

Your question doesn’t make any sense the way it is. This is what I was trying to get you to clarify in the other thread you started on this problem.

Do you mean how long does it take (in days) one mole of electrons to flow through the cross-section, or do you mean how many moles of electrons flow through the cross-section in one day? These are not the same thing, although the calculation will be nearly identical.

I’m guessing it is supposed to read more like “How long does it take 1 mole of electrons to flow through a cross section of the wire, in days?” Please tell me if this is the right interpretation.

The units of your answer is not in days, it is in moles/day. Try taking the inverse of the 0.366 you found, I suspect that will give you the right answer. What you have calculated is 0.366 moles/day (i.e. 0.366 moles will pass through the cross-section in 1 day). What I think you want is how many days will it take for one mole to pass through the cross-section. Can you see what I’m getting at?

You need to make sure your units work out properly when you do this calculation. I think that is likely what is causing the problem here.

Remember that it is 6.022x10^23 electrons/mole. The mole counts as a unit when you are doing this. So be aware of that when you are dividing.

 

[fsm]

Sorry about the confusion. I forgot the s in days. I started a new thread on this because through my own fault made the problem too confusing. I guess I did it again . What I did wrong was I should have divided the constant of a mole by the electron current. This gives moles per second. Then divide that answer by 86400 to get 1 mole in x days which was 2.73 days. Thanks for the help and sorry for the confusion.

 

[hage567]

Sorry about the confusion. I forgot the s in days. I started a new thread on this because through my own fault made the problem too confusing. I guess I did it again . What I did wrong was I should have divided the constant of a mole by the electron current. This gives moles per second. Then divide that answer by 86400 to get 1 mole in x days which was 2.73 days. Thanks for the help and sorry for the confusion.

Glad it's all figured out!