# What is the mobility and conductivity of free electrons in metals

1.1 The concentration of free electrons and free electrons
Why do metal materials have the ability to conduct electricity? The answer can be obtained from the structure of matter. For example, a copper atom has 29 electrons outside its nucleus. These electrons are distributed in layers. There is only one electron in the layer furthest from the nucleus, which has the weakest binding force to the nucleus. It is easy to be affected by the neighboring nucleus, and break away from the atom to which it originally belonged, and become an electron that does not belong to any atom but belongs to the entire crystal. Such electrons can move in the entire crystal, and people call such electrons “free electrons”. At room temperature, there are 8.45×1022 copper atoms per cubic centimeter of copper crystal (the copper unit cell model is shown in Figure 1-1). Each copper atom has one electron into a free electron, and obviously there are 8.45×1022 electrons per cubic centimeter. Based on the same analysis, we can also know that in other conductors, the concentration of free electrons per cubic centimeter of crystal is also very high.

Figure 1-1 copper unit cell model
1.2 Mobility and conductivity of free electrons
Because there are a large number of constantly vibrating atoms and a large number of freely moving electrons in the crystal, it is inevitable that the movement of any one electron often encounters other atoms and electrons, and each collision will change its direction of movement. Therefore, the movement of these free electrons in the crystal is chaotic. If a certain external voltage is applied to both ends of the metal, the movement of free electrons will be affected by the electric field force. Although it will still collide with other atoms and electrons in motion, it will accelerate in the direction of the electric field force under the action of the electric field after each collision (the electron is negatively charged, and the direction of the electric field force is exactly the direction of the electric field. On the contrary), the overall result of its motion is as if free electrons are moving in a straight line in the direction opposite to the electric field. If there is a linear motion, there is a linear velocity. Obviously, the linear velocity is proportional to the electric field strength. People call the linear velocity per unit electric field strength (the voltage difference per centimeter of length is 1V, that is, 1V/cm) the “mobility” of free electrons, which is represented by u.
When a voltage is applied to a conductor, the free electrons in it will migrate from one end of the conductor to the other end at a certain speed, that is, the charge flows from one end to the other end. This is the process by which a conductor conducts current. Obviously, the conductivity of an object depends on the concentration of free electrons (indicated by n, the unit is cm-3) and its mobility u (unit: cm2/(SV) )]the size of. In order to illustrate the conductivity of objects, the concept of “conductivity” is introduced, namely:

σ=enu

In the formula, e is the charge carried by the electron. The reciprocal of conductivity is called resistivity.