Determining drift velocity of electrons at specific temperature

[mlbqd3]

Homework Statement

A gold conductor with an electric field of 0.01 V/m applied, is 0.01 m long and 5.0E-5m in radius. Assuming one conduction electron per atom, what is the drift velocity of the electrons at a temperature of 20.0 degrees C? at 50 degrees C?

Homework Equations

I know that R=rho(L/A), but I have no idea where to go from here. If someone could give me an idea how to connect the length and area to drift velocity I would appreciate it.

 

[Nate810]

The Attempt at a SolutionI have not attempted to solve this problem because I do not know how to start.

 

[nlightner]

To determine the drift velocity of electrons at a specific temperature, we can use the equation for current density, J = nevd, where n is the number of conduction electrons per unit volume, e is the charge of an electron, v is the drift velocity, and d is the cross-sectional area of the conductor. We can also use Ohm's law, V = IR, where V is the applied voltage, I is the current, and R is the resistance of the conductor.

In this case, we are given the length and radius of the gold conductor, so we can calculate the cross-sectional area using A = πr^2. We are also given the applied electric field, which we can use to calculate the resistance using Ohm's law.

To determine the number of conduction electrons per unit volume, we can use the density of gold, which is approximately 19300 kg/m^3, and the atomic mass of gold, which is 196.97 g/mol. This can be converted to the number of atoms per unit volume using Avogadro's number, and then multiplied by the number of conduction electrons per atom, which is 1.

Once we have all the necessary values, we can plug them into the equation for current density and solve for the drift velocity. This will give us the drift velocity of electrons at 20.0 degrees C.

To determine the drift velocity at 50 degrees C, we can use the relationship between temperature and resistivity, ρ = ρ0(1 + α(T - T0)), where ρ0 is the resistivity at a reference temperature T0 and α is the temperature coefficient of resistivity. We can use this equation to calculate the resistivity at 50 degrees C, and then repeat the steps above to calculate the drift velocity at this temperature.

I hope this helps to guide you in solving this problem. Please let me know if you have any further questions.