What is the average time between collisions for conduction electrons in copper?

In summary, the conversation is discussing how to compute the average time between collisions for conduction electrons in copper. The equations Vd=-e*E*T/(Me) and Vd=I/PA are mentioned, along with the given information of a copper wire's diameter, current, and mass density. Hints are provided to help solve the problem, and the final solution involves finding the electric force using the current density and resistivity of copper.
  • #1
jromega3
27
0

Homework Statement


compute the average time between collisions T for conduction electrons in copper.


Homework Equations


Vd=-e*E*T/(Me)
Where e is electron's charge
E is electric Field
T is what I'm solving for
And Me is mass of the electron

Vd=I/PA


The Attempt at a Solution



so it was given that a copper wire with a 1.0mm diameter had a current of 1A...and it's mass density is 8900kg/m^3.
So m= 1 electron(8900kg/m^3)(6.02X10^23 atoms/0.0635kg) = 8.4 X 10^28/m^3
So
Vd=1A/(8.4X10^28 m^-3)(1.6X10^-19C)(7.9x10^-7m^2) = 9.4 x 10^-5 m/s

So now...
Vd=-e*E*T/(Me)

So T=(Vd)(Me)/(-e)(E)
I have Vd, Me is mass of the electron, and -e is charge of the electron. I need the electric force...and am stumped. How do I get it from the given info? Thanks for the help.
 
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  • #2
Current density J = I/A, And resistivity of the material rho = E/J.
E = rho*I/A. For copper rho = 1.72x10^-8ohm.m
Vd = J/nq, where n is electron density in copper = 8.5x10^28 m^-3.
See whether these hints helpful to solve the problem.
 
  • #3
Ok, so I get E=rho*J.....or since I don't know J J is also Vd*nq...so I get E=rho*Vd*nq...
so my equation becomes T=(Vd)(Me)/(-e)(rho)(Vd)(Nq)
stuff cancels and I get Me/(-e)(rho)(Nq) and I get a really wrong number. hmm
Edit. Nevermind...my bad. We Have I and A can be easily solved giving J. Thanks again, always appreciated.
 

FAQ: What is the average time between collisions for conduction electrons in copper?

What is the definition of "time between collisions"?

The time between collisions is the average duration between two successive collisions of a particle or object in a given system. It is a measure of how often collisions occur in a system.

How is the time between collisions calculated?

The time between collisions can be calculated by dividing the average speed of the particles in the system by the total number of collisions that occur in a specific time frame. It can also be calculated by taking the reciprocal of the collision frequency, which is the number of collisions per unit time.

Does the time between collisions depend on the type of particles in the system?

Yes, the time between collisions is influenced by the properties of the particles in the system, such as their mass, size, and shape. Particles with larger masses or sizes tend to have longer times between collisions as they have more momentum and take longer to traverse a given distance.

How does temperature affect the time between collisions?

Temperature plays a significant role in determining the time between collisions. As temperature increases, the average speed of particles also increases, resulting in a decrease in the time between collisions. This is because the particles are moving faster and therefore, colliding more frequently.

Can the time between collisions be changed?

Yes, the time between collisions can be altered by changing the properties of the system, such as temperature, pressure, and particle size. For example, increasing the temperature or decreasing the particle size can decrease the time between collisions, while decreasing the temperature or increasing the particle size can increase the time between collisions.

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