This document provides an overview of classical free electron theory, including its history, assumptions, limitations, successes, and basic terms. It was introduced in 1900 by Drude and further developed by Lorentz in 1909. The theory assumes electrons in metals move freely and collide elastically with fixed positive ions. While it could explain electrical conductivity and behavior in magnetic fields, it had limitations such as not explaining specific heat capacities and why only some materials are metallic. The advent of quantum free electron theory in 1928 by Sommerfeld addressed some of these issues and limitations.

1. EXPLORING THE
CLASSICAL FREE
ELECTRON THEORY :
AN ANALYSIS OF
ITS SUCCESS,
LIMITATIONS,
ASSUMPTIONS

2. COMPONENTS
• INTRODUCTION
• HISTORY
• ASSUMPTIONS OF CFET
• LIMITATIONS OF CFET
• SUCCESS OF CFET
• BASIC TERMS INVOLVED IN
CFET

3. INTRODUCTION
• Classical free electron theory is
a fundamental concept in
quantum mechanics.
• This presentation explores the
assumptions, successes, and
limitations of this theory.
• The aim is to deepen our
understanding of the theory
and its impact on modern
physics.

4. HISTORY
INTRODUCED BY P.
DRUDE IN 1900
DEVELOPED BY LORENTZ
IN 1909

5. ASSUMPTIONS OF CLASSICAL FREE ELECTRON
THEORY
1
CFET is based
on the
following
assumptions
2
The valence
electrons of
atoms are free
to move about
the whole
volume of the
metal
3
The free
electrons
move in
random
direction and
collide with
either positive
ions fixed to
the lattice
4
All the
collisions are
elastic in
nature i.e.,
there is no loss
of energy.
5
The
momentum of
free electrons
obeys the laws
of the classical
kinetic theory
of gases.
6
The electron
velocities in a
metal obey
classical
Maxwell-
Boltzmann
distribution of
velocities.
7
When the
electric field is
applied , the
free electrons
are
accelerated
opposite to the
direction of
applied electric
field.
8
The mutual
repulsion
among the
electrons is
ignored,
so they move
in all direction
with all
possible
velocities.
9
The movement
of free
electrons
inside a metal
is equivalent to
the motion of
free electrons
in a potential
10
These are the
assumptions
of CFET

6. LIMITATIONS
OF CLASSICAL
FREE
ELECTRON
THEORY
It cannot explain why only
some crystals are metallic in
nature.
It cannot explain why the
metals prefer only certain
structure e.g. Fe is cubic
while Zn is hexagonal.
It cannot explain why the
observed specific heat of
metals is only 1% of the
calculated value (i.e., 3/2 N
KB; N are number of free
electrons per gram atom).
It cannot explain the
temperature variation of the
electrical conductivity.
It cannot explain the
paramagnetic behaviour of
metals.
It also could not explain the
occurrence of long mean
free paths at low
temperatures.

7. SUCCESS OF CLASSICAL FREE
ELECTRON THEORY
• Despite its limitations, classical free
electron theory has been successful in
explaining some important
phenomena. For example, it can
explain the electrical conductivity of
metals and the behavior of electrons
in a magnetic field. The theory has also
been used in the development of
modern technologies like
semiconductors and transistors.

8. BASIC
TERMS
INVOLVED
IN CFET
• DRIFT VELOCITY
• MOBILITY
• MEAN FREE PATH
• MEAN COLLISION TIME
• RELAXATION TIME
• BAND GAP
• CURRENT DENSITY

9. Drift Velocity (Vd)
• The drift velocity is defined as the average velocity
acquired by the free electron in particular direction,
due to the applied electric field.
Mobility
The mobility is defined as the drift velocity (Vd)
acquired by the electron per unit electric field (E)
Mean free path
The average distance travelled
by a electron between two
successive collision is called
mean free path.

10. Mean collision time (or) Collision time
• It is the time taken by the free electron between two
successive collision.
Relaxation time
• It is the time taken by the electron to reach equilibrium
position from disturbed position in the presence of electric
field where l is the distance travelled by the electron. The
value of relaxation time is of the order of 10–14 sec.
Band gap (Eg)
• Band gap is the energy difference between the minimum
energy of conduction band and the maximum energy of
valence band.

11. Current density (J)
It is defined as the current per unit area of cross section of an
imaginary plane hold normal to the direction of the flow of current in
a current carrying conductor.

12. ADVENT OF
QUANTUM FREE
ELECTRON THEORY
:
• Quantum free electron theory was
proposed by Sommerfeld in 1928.
• It overcomes many of the drawbacks of
classical theory.
• Sommerfeld explained them by
choosing Fermi Dirac statistics instead
of Maxwell-Boltzmann statistics
• . He developed this theory by applying
the principles of quantum mechanics.
Assumptions of Quantum Free Electron
Theor This Photo by Unknown author is licensed under CC BY-SA.

13. THANK YOU !
SUBMITTED BY :
THARANYA S
ECE – D
22ECR216