How Long for an Electron to Move 1cm in a Silver Wire?

[GreenDinos]

A silver wire of diameter 1 mm carries a current of 130 mA. The density of conduction electrons in silver is 5.8X10^28 m-3. How long (on average) does it take for a conduction electron to move 1.0 cm along the wire?

ok, so first I calculated drift speed using the equation Vd = I/ Ne * A

for Area, I just used pi*r^2

I set it up Vd = .130A/ ((5.8e28 m^-3) x (7.853e-7 m^2)) and got the drift speed to be 2.8538e-24 m/s

I then set up 2.8538e-24 m/s x 100cm/m x 60sec/min and got
1.71228e-20cm/ min .

To get minutes for one cm i took
1cm/1.71228e-20cm/ min and got 5.840e19 minutes to move one cm.

i'm obviously doing somehting wrong because it's not accepting my answer. Is there something I'm missing??

 

[ehild]

A silver wire of diameter 1 mm carries a current of 130 mA. The density of conduction electrons in silver is 5.8X10^28 m-3. How long (on average) does it take for a conduction electron to move 1.0 cm along the wire?

ok, so first I calculated drift speed using the equation Vd = I/ Ne * A

You left out the charge of the electrons. Neglecting signs,
$$v_d=\frac{I}{A q N_e}\mbox{ , q = }1.6\cdot10^{-19}\mbox{ C. }$$

ehild

 

[M98Ranger]

Hi there,

I can see that you have correctly calculated the drift speed of the conduction electrons in the silver wire. However, there may be a mistake in your conversion from meters to centimeters. The drift speed you calculated is in meters per second, so when converting to centimeters, you should use a conversion factor of 100 (not 100cm/m). This would give you a drift speed of 2.8538e-22 cm/s.

Using this value, the time taken for a conduction electron to move 1 cm along the wire would be:

1cm / (2.8538e-22 cm/s) = 3.504e21 seconds

This is a very large number, so it is often more convenient to express it in a different unit, such as minutes or hours. To convert seconds to minutes, you can divide by 60, so the time taken would be:

(3.504e21 seconds) / 60 seconds/min = 5.84e19 minutes.

I believe your answer was correct, but there may have been a mistake in the conversion from meters to centimeters. I hope this helps clarify and if you have any further questions, please let me know.