PHYSICS UNIT-2....

                                              UNIT-2 


                                  ELECTRON THEORY OF METALS 


  INTRODUCTION: 
--------------------------
      In metals the valence electrons are loosely bound to their individual atoms. They move 


      randomly in different directions and are called free electrons. Hence, the valence 


      electrons of the atoms become the conductors of electricity in metals and they are 


      known as conduction electrons 


   ♣ The electron theory of solids explains the structure and properties of solids. The theory 


     is applicable to all solids (all metals and non metals). It explains the electrical, thermal 


     and magnetic properties of solids. The theory has been developed in three main stages. 


   ♣ The Classical free electron theory: This theory developed by LORENTZ & DRUDE in 


     1900. According to this theory the free electrons of the metals obey the classical 


     mechanics. 


   ♣ The Quantum free electron theory: SOMMERFELD developed this theory during 


      1928. According to this theory the free electrons obey quantum laws such that the 


      wave nature of electrons is taken into account. 


  ♣The Band theory or Zone theory: In 1928 BLOCH started this theory in which 


     electrons move in a periodic field provided by the lattice. The concept of hole, origin of 


     band gap and effective mass of electrons are the special features of this band theory. 


  PROPERTIES OF THE METALS: 


      ♣ Metals have high electrical conductivity σ. 


      ♣ Metals obey ohms law i.e. the current flowing along a wire is proportional to the p.d 


        between the ends of the wire. V=iR 


      ♣ If l is length and A is area of cross section of the wire then its resistance is given by 


                  l 
           R = ρ      Where ρ is called resistivity of the material. 
                  A 


      ♣ Ohm‟s law can also be expressed in terms of current density (J) and electric field 


        strength is given by     J =σ E    Where σ =      is the conductivity 


      ♣ Good electrical conductors are also good thermal conductors. According to 


        Wiedemann Franz law     = constant 


        where K is thermal conductivity of the metal 

CLASSICAL FREE ELECTRON THEORY: (or) Salient features of Classical freee 


      electron theory: 


      LORENTZ AND DRUDE Proposed a theory comparing the electrons with the 


      orientations of the gas molecules in space. So this is also known as free electron gas 


      model 


      Postulates:- 


     ♣ The valence electron of atoms are free to 


        move in the metals like the gas molecules 


        in a container. 


     ♣ In the absent of electric field the electrons 


        move randomly in all possible directions 


       and the net current is zero. 


     ♣ While moving, the electrons suffer 


        collisions among themselves. All the 


        collisions are elastic. 


      ♣ Between any two collisions, the electrons 


          move with uniform velocity. 


      ♣ Applying kinetic theory to the electron gas, the root mean square velocity of the 


        electrons are given by          Vrms= /,


      ♣ The electron speeds are distributed according to Maxwell Boltzmann distribution 


         law. 


      ♣ The electrostatic force of attraction between positive ion cores and free electrons, 


        the electrostatic force of repulsion between the electrons is neglected. 


      ♣ The free electrons are confined to the metal due to surface potential. 


      ♣ In the presence of electric field, the free electrons are accelerated in a direction 


         opposite to the direction of the electric field 


      ♣The electrons acquires velocity due to application of external electric field is known as 


          „drift velocity „ (V ) 
                             d 


      DERIVATION OF OHM’S LAW BASED ON FREE ELECTRON THEORY :- 


      ♣ Suppose E is the potential difference applied across a conductor of length L and 


        cross  sectional area „A‟ 


      ♣Let Vd  is the average drift velocity and n is the electron density (no. of electrons per 


         unit volume). 


      ♣Therfore current density          J = -neVd       -------->(1)