Free Electrons Theory : Assumptions , Success Drawbacks SSP-2 cover by midnight talks

Free elecrtrons theory is important in terms 

• To explain the properties of materials
• To explain the thermal, eectrical and magnetic properties of solids 

There certain approximations approached in theory of free electrons 

1. Free electron approximation in which electrons are freely move while atoms are fixed
2. Tightly Bound Approximation in which electrons are fixed while atoms are freely moving

An abbreviated photo of atom

As we discuss approximations related to Free electron theory , the theory of Free electrons can be summarised in two events when classical physics was universal in its majesty. 

Firstly Drude and Lorentz in 1900 stated classical free elctrons theory as

                   

                                  ''Matels contain free electrons and obey 

                                                       the rules of classical mechanics.''

Note: in this topic we shall cover the postulates of Classical theory of free electrons only

Then with accurate results new theory termed as quantum free electrons theory given by Summerfield in 1928 stated;

                                   ''Free electrons obey the quantum laws and

                                                              moving with constant potential''.

 

Postulates of Clasical Theory of free electrons

1:-The electrons in valence shell in atom are free to move about the whole volume of material. In a gas container, atoms moving randomly is a good example to imagine the motion of valence shell electrons.

2:-The free electrons move in random direction and collide with either positive ions fixed to latticeor the other free electrons. All collisions are elastic in nature i.e. no loss of energy. 

3:-The momentum of free electrons obey the laws of classical kinetic theory of gases.

4:-The Veocity of electrons in metals obey Boltzman distribution of velocities. 

5:-When electric electric field is applied to the matter , the free electrons are accelrated in the direction opposite to the applying electric field. 
6:-Coloumb law say that mutual repusion between electrons is ignored so that they move in all directions with all possible velocities. 
7:-In the sense of electric field the energy associated with electrons at temperature t is  given in relationship of kinetic theory of energy as give below

Achievements of Classical Theory of Free Electrons

1:-It verify's ohm's law.

2:-It explains the thermal conductivity of metals.

3:-Optical properties of metals are explained by these models.

Drawbacks of Classical Theory of Free Electrons

1:-Electrical conductivity of semiconductors could not be explained .It fails to explain specific heat and specific heat capacity of metals.                          

                                                         Cv=∂u/∂t

2:-Feromagnetism could not be explained.

3:-Fails to explain the semi conducting properties of metals.

Quantum Theory of Free elecrtrons 

See Link....

Regards: ADeel