UNIT-2
ELECTRON THEORY OF METALS
INTRODUCTION:
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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)
