Unit No-3
Quantum Physic
WAVE PARTICLE DUALITY
WAVE PARTICLE DUALITY
Introduction
The wave theory of light successfully explained the optical phenomenon like
reflection, refraction, interferences, diffraction, and polarization but it failed to explain the
phenomenon of photoelectric effect and Compton Effect. These phenomena were explained
on the basis of quantum theory. According to quantum theory a beam of light of a
frequency v consist of small packets each having energy hv called photon or quanta. These
photons behave like particles. Thus light possesses dual nature. Sometime it behaves like a
wave and sometime like a corpuscle.i.e.Particle.
In short, to explain the photoelectric effect and Compton Effect we must treat
electromagnetic radiation as particle. Even though it is essential to assign both wave and
particle aspect to electromagnetic radiation, in any experimental situation one model can be
applied. Never both! Accordingly, In 1928 Neil Bohr started the principle of
complementarily. The wave and particle aspects of electromagnetic radiation are
complementarily. Bohr's principle of complementarily is applicable to the dual nature wave
and particle of material particles such as electrons, photons and others. The measurement of
elm and other characteristics of cathode ray clearly established the particle aspects of the
electrons.
Whereas electrons or any other material particles nmust be assigned wave of de
Broglie wavelength in order to explain the diffraction of material particles. When we speak of
photons we know that it is the electromagnetic wave that is associated with them. In case of
material particles, we know their wavelength from the de-Broglie hypothesis, but we do not
know the nature of these waves. The wave, which guide the motion of particles, are called
Matter wave.
De Broglie Hypothesis
According to de Broglie, a moving particle whatever its nature, has wave associated
with it. De Broglie postulated that a free particle with rest mass m' moving with non
relativistic speed y' has a wave associated with it. The wavelength of such a wave is given
by
h
my
where 'h' isPlank's constant.
De Broglie Wavelength by Analogy with Radiation
By Planck'squantum theory of radiation, the energy of a photon is given by,
E= hu .......1)
where h isPlanck's constant and v is the frequency of radiation.
According to Einstein's theory of relativity,
E= me ....2)
ZCOER STUDY MEDIA
, where E is the energy equivalence of mass 'm' and c is the velocity of light.
From equations (1) and (2), we have
hu = me²
C
But
hc = me
h
.......(3)
mC
If p is the momentum of a photon, then
p = mc
From equation (3), we get,
=
......(4)
P
De Broglie carried these consideration over to the dynamics of a particle, and said that
the wavelength of the wave associated witha moving particle having a momentum mv is
given by
h h
•......(5)
my
From above equation (5) we see that the wavelength of radiation is related to the momentum
of photon through plank constant. De-Brogile put forward an outstanding idea in 1924
that nature must have a fundamental symmetry and hence above equation (5) must be
true for photon as well as material particle.
Question: State de-Broglie hypothesis (2M)
De Broglie Wavelength in terms of Kinetic Energy
If the particle of mass 'm' is moving with speed 'v', its kinetic energy is given by,
E=mv .....1)
1
Or E= m'y2
2m
E=
p (p= mv)
2m
p'= 2mE
p= /2mE .....2)
, The de Broglie wavelength associated with a moving particle is given by
h
......3)
From (2) and (3), we get,
=
V2mE
.....3)
De-Broglie Wavelength of an Electron
If a charged particle say an electron is accelerated through a potential difference of V
volts then the kinetic energy of the electron is
E= eV ......(1)
The wavelength of an electron in terms of kinetic energy is
h
V2mE
Or =
V2meV
If m, is the rest mass of electron, then
h
= .......(2)
V2moeV
Now, h=6.625 X 10** Js
m, = 9.1X 10 Kg
e= 1.6X 10 C
Hence, putting these values in equation (2), we get,
-A° .....3)
Question:
1.State de-Broglie hypothesis of Matter wave. Show that de-Broglie wavelength
of a charged particle is inversely proportional to the square root of the
accelerating potential. (6M)
2. State de-Broglie hypothesis of Matter wave. Derive an expression for de
Broglie wavelength in term of Kinetic Energv. (6M)
Quantum Physic
WAVE PARTICLE DUALITY
WAVE PARTICLE DUALITY
Introduction
The wave theory of light successfully explained the optical phenomenon like
reflection, refraction, interferences, diffraction, and polarization but it failed to explain the
phenomenon of photoelectric effect and Compton Effect. These phenomena were explained
on the basis of quantum theory. According to quantum theory a beam of light of a
frequency v consist of small packets each having energy hv called photon or quanta. These
photons behave like particles. Thus light possesses dual nature. Sometime it behaves like a
wave and sometime like a corpuscle.i.e.Particle.
In short, to explain the photoelectric effect and Compton Effect we must treat
electromagnetic radiation as particle. Even though it is essential to assign both wave and
particle aspect to electromagnetic radiation, in any experimental situation one model can be
applied. Never both! Accordingly, In 1928 Neil Bohr started the principle of
complementarily. The wave and particle aspects of electromagnetic radiation are
complementarily. Bohr's principle of complementarily is applicable to the dual nature wave
and particle of material particles such as electrons, photons and others. The measurement of
elm and other characteristics of cathode ray clearly established the particle aspects of the
electrons.
Whereas electrons or any other material particles nmust be assigned wave of de
Broglie wavelength in order to explain the diffraction of material particles. When we speak of
photons we know that it is the electromagnetic wave that is associated with them. In case of
material particles, we know their wavelength from the de-Broglie hypothesis, but we do not
know the nature of these waves. The wave, which guide the motion of particles, are called
Matter wave.
De Broglie Hypothesis
According to de Broglie, a moving particle whatever its nature, has wave associated
with it. De Broglie postulated that a free particle with rest mass m' moving with non
relativistic speed y' has a wave associated with it. The wavelength of such a wave is given
by
h
my
where 'h' isPlank's constant.
De Broglie Wavelength by Analogy with Radiation
By Planck'squantum theory of radiation, the energy of a photon is given by,
E= hu .......1)
where h isPlanck's constant and v is the frequency of radiation.
According to Einstein's theory of relativity,
E= me ....2)
ZCOER STUDY MEDIA
, where E is the energy equivalence of mass 'm' and c is the velocity of light.
From equations (1) and (2), we have
hu = me²
C
But
hc = me
h
.......(3)
mC
If p is the momentum of a photon, then
p = mc
From equation (3), we get,
=
......(4)
P
De Broglie carried these consideration over to the dynamics of a particle, and said that
the wavelength of the wave associated witha moving particle having a momentum mv is
given by
h h
•......(5)
my
From above equation (5) we see that the wavelength of radiation is related to the momentum
of photon through plank constant. De-Brogile put forward an outstanding idea in 1924
that nature must have a fundamental symmetry and hence above equation (5) must be
true for photon as well as material particle.
Question: State de-Broglie hypothesis (2M)
De Broglie Wavelength in terms of Kinetic Energy
If the particle of mass 'm' is moving with speed 'v', its kinetic energy is given by,
E=mv .....1)
1
Or E= m'y2
2m
E=
p (p= mv)
2m
p'= 2mE
p= /2mE .....2)
, The de Broglie wavelength associated with a moving particle is given by
h
......3)
From (2) and (3), we get,
=
V2mE
.....3)
De-Broglie Wavelength of an Electron
If a charged particle say an electron is accelerated through a potential difference of V
volts then the kinetic energy of the electron is
E= eV ......(1)
The wavelength of an electron in terms of kinetic energy is
h
V2mE
Or =
V2meV
If m, is the rest mass of electron, then
h
= .......(2)
V2moeV
Now, h=6.625 X 10** Js
m, = 9.1X 10 Kg
e= 1.6X 10 C
Hence, putting these values in equation (2), we get,
-A° .....3)
Question:
1.State de-Broglie hypothesis of Matter wave. Show that de-Broglie wavelength
of a charged particle is inversely proportional to the square root of the
accelerating potential. (6M)
2. State de-Broglie hypothesis of Matter wave. Derive an expression for de
Broglie wavelength in term of Kinetic Energv. (6M)
