Question

The electron drift speed in a 3.00 mm diameter gold wire is 5.00*10^-5 m/s. How long does it take 1 mole of electrons to flow through a cross section of the wire?

Answer 1

Concepts and reason

The concepts used to solve this problem are drift velocity, the relationship between current and drift velocity, and Avogadro’s constant.

Initially, use the relationship between current and drift velocity due to the motion of electrons, then use the relative number of electron passed through the cross section of wire. Compare the current due to motion of free electrons in a wire and current due to the number of free electron passed through the wire. Calculate the total number of free electrons in 1 mole of gold wire by using Avogadro’s law. Finally, calculate the time taken by the electron to flow through a wire.

Fundamentals

The relationship between current and drift velocity is:

$I=nAeva $

Here, I is the current produced due to the motion of free electrons in a conductor, n is the number of free electrons per unit volume, A is the area of cross section of the wire, e is the charge of electrons, and is the drift velocity of electrons.

The expression for the current produced due to the number of free electrons passing through the cross section of wire per unit time is:

Here, N is the total number of free electrons passing through 1 mole of gold wire and t is the time taken by 1 mole of electrons to flow through the wire.

The number of free electrons flowing through the gold wire per unit volume is .

The relationship between the current and drift velocity in a conductor is:

$I=nAeva $ …… (1)

The expression for the current produced due to the number of free electrons through the wire is:

…… (2)

Compare the equation (1) and (2) to find the time taken by the electrons to flow.

Substitute for A in terms of t.

Here, d is the diameter of the gold wire.

The expression for the time taken by the electrons to flow through the conductor is:

Substitute for N, for n, for d, and for to find t.

Ans:

The time taken by the electrons to flow through a cross section of the wire is.