D) Describe the simplified picture of electron transport (electrons colliding with ions, distribution of energy) and derive the equation for current density and conductivity. E) How does the specific heat of the metal is defined in
Consider the diagram below for this question;
Here, we have a conductor in which electrons perform random motion.
The path of one of the electron performing random motion is shown in the diagram.
When the potential difference was zero across the ends of the conductor, the net displacement of the electron was zero as there was no external force or field acting on it.
As soon as a potential difference is applied across the ends of the conduction, some amount of electric field will apply force on the electron and due to which, this electron will have a small drift from the path of its motion.
The electron will go on colliding with the other electrons.
The path between two consecutive collisions will be known as the free path and the mean of all such paths during the entire of motion of electrons inside the conductor is called the mean free path.
The time between two successive collisions is called relaxation time.
And the velocity due to the small drift after application of potential difference across the ends of the conductor is called the drift speed / velocity of that electron.
Force on the electron due to the external applied electric field is given by the equation;
(Here, e is the charge on an electron)
Thus, the acceleration on that electron will be (Here, m is the mass of electron)
The value of this acceleration will be very small
Now, we can write the equation for the drift velocity of this electron as;
Here, is the relaxation time
We consider the average initial velocity of all the electrons to be zero as there was no displacement before applying the external supply
Step by step
Solved in 5 steps with 1 images
