My book mentions that when an electric field is applied to a conductor the electrons get accelerated in a direction opposite to that of the field. These electrons however collide with the atoms on the lattice of the metal. What actually happens in the collision? Is any other electron ejected from the atom during this collision? I also want to know about drift velocity, mean free path and relaxation time.
What actually happens in the collision?
When electrons collide with atoms they lose their speed and kinetic energy, which turns into heat.
Is any other electron ejected from the atom during this collision?
Not to my knowledge. In general, ionization requires a lot of energy, i.e., very strong electric field and long free path. Also, it would not likely to make any difference, since metals already have plenty of free electrons for good conductivity.
I also want to know about drift velocity, mean free path and relaxation time.
Those terms are defined in many sources, so you can google it for details, so, I'll just try to give you the gist of it.
The electrons are constantly moving in random directions and are colliding with atoms. Because of the randomness, their average velocity is zero.
When the electric field is applied, the electrons continue their chaotic movement, but the direction against the field becomes dominant and, therefore, they acquire some non-zero average velocity in that direction. It is called drift velocity. The drift velocity is proportional to the electric field and it defines the current.
The mean free path, as applied to electrons, is just the average distance an electron travels between successive collisions with atoms and the relaxation time is the average time between these collisions. The relaxation time directly affects the conductivity, because, given an electric field, the drift velocity, and, therefore, the current, is proportional to the relaxation time.
First, when an electric field is applied to a metal conductor, as per QM the electric field's force is mediated by virtual photons, they interact with the electrons of the metal.
These electrons in the metal are not free. They are loosely bound to the atoms of the lattice of the metal. Because they are loosely bound, they can move from one atom to another atom.
As the electric field interacts with the electrons in the metal, the virtual photons' energy is given to the electron's kinetic energy, and so these loosely bound electrons start moving inside the metal, from one nucleus to another.
The speed as these loosely bound electrons move from one atom to another atom is called drift velocity. It is very slow. Though, since the electrons in the metal are really densely packed, the actual speed of electricity is close to the speed of light.
These loosely bound electrons are not free, they are always bound to nuclei, as per QM they exist at a certain energy level around the nucleus, in the valence band, which is the conduction band too, in metals.
Mean free path is the average distance traveled by the electrons from one nucleus to another nucleus.
Now these loosely bound electrons in a metal have a random thermal motion regardless of the electrical field. But if an electrical field is applied, then there will be a drift velocity in the direction of the electric force, superimposed on the random thermal motion. That is why this drift velocity is so slow.
The relaxation time in this case is the collision time, that is the average time between collisions. These collisions are inelastic scattering.
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