# Free Electron Theory of metals

I don't quite get the concept of drift velocity. According to definitions, it is the net velocity with which the electrons are drifted in a direction opposite to the applied electric field. Is the thermal velocity included in that or is it different? According to what I have read drift velocity goes to zero after each collision but thermal velocity still remains right? And how does it differ from the root mean square velocity of the electrons? Can someone please explain this to me ?

## 2 Answers

You can consider the mobile electrons as having random thermal motion (speeds of the order $$10^5 \rm m\,s^{-1}$$) with a mean drift velocity due to the application of an electric field (speeds of the order of fractions of $$\rm mm\,s^{-1}$$) superimposed on the random thermal motion.

The random thermal motions are essentially random. In a given time window, the average motion to the right is equal to that of left and so on for all other directions. So in that time window, the average motion is zero.

However in the presence of an electric field say pointing left to right, then in a given time window, the average motion to the left is greater than that to the right (greater the field greater the discrepancy). This results in a net motion towards the left.

An analogy would be the flowing river. Each water molecule in the river is moving randomly (thermal motion). But there is a net motion in the direction of the flow of the river as governed by the topography (gravity essentially).