Simple drift speed probem driving me nuts

[ttran1117]

Homework Statement

A current of 200 mA flows in a silver wire of radius 0.8mm. Find (a) the drift speed of the electrons. (b) the number density of particles.

Homework Equations

The Attempt at a Solution

The answer in the book is 1.07 x 10^-5, but I'm getting 1.06 x 10^-4. Can anyone tell me what I'm doing wrong?

So, I have J = I/A and J=nev_d ==> v_d = J/(ne)
J = 200 x 10^-3/pi(0.8x10^-3)^2

n = p*Avg/M
= 1.05 * 6.022 x 10^23 / 107.868 x 10^-3

plugging in for v_d, I get 1.06 x 10^-4.

This problem is supposed to be simple, but it's driving me nuts! Someone help please! Thanks a lot

 

[ehild]

You used wrong value for the density of silver.

ehild

 

[tomcue]

It looks like the issue may be with your calculation for the number density of particles. The equation you used, n = p*Avg/M, is for calculating the number density of a gas, not for a solid material like a silver wire. Instead, you should use the equation n = N/V, where N is the number of particles and V is the volume of the wire.

To find N, we can use the formula N = nA, where n is the number of electrons per unit volume (the atomic density) and A is the cross-sectional area of the wire. Since we are dealing with a solid material, we can assume that the number of electrons per atom is equal to the number of protons, so n = Zp, where Z is the atomic number and p is the number of protons.

Plugging in the values, we get N = (47 x 6.022 x 10^23) x (pi(0.8x10^-3)^2) = 1.07 x 10^20.

Now, we can plug this value for N into the equation n = N/V and solve for n. V is equal to the volume of the wire, which can be calculated using the formula V = pi(0.8x10^-3)^2 x L, where L is the length of the wire. Let's assume a length of 1 meter for simplicity, so V = pi(0.8x10^-3)^2 x 1 = 5.03 x 10^-7 m^3.

Plugging in the values, we get n = (1.07 x 10^20)/(5.03 x 10^-7) = 2.13 x 10^26 m^-3. This is the correct value for the number density of particles, which when used in the equation v_d = J/(ne), gives us the correct answer of 1.07 x 10^-5 m/s for the drift speed.

I hope this helps clear up any confusion and solves the problem for you. If you have any further questions, please don't hesitate to ask. Keep up the good work!