Dual Nature of matter and radiation
Light, the electromagneticradiation, possesses dual character of a particle as well as a wave. The
wave-particle duality is only the concept of energy transmission of radiation. When we talk
about particle concept,it is easy to understand and must described by its properties like mass,
velocity, momentum, energy and a definite position in space. The phenomena like photoelectric
effect, Compton effect take place due to interaction of radiation as particle with matterwhich
evidently has particle properties. Planck’s quantum theory quanta successfully explains these
phenomenon. On the other hand, wave concept is comparatively difficult to understand. Unlike
particle, a wave is like a disturbance which spreads out over a large region. It cannot be located
here or there. It is specified by its wavelength, frequency, amplitude, energy and momentum.
Various optical phenomenon such as interference, diffraction and polarization strongly validate
the wave character of electromagnetic radiation.Hence from the above facts it can be said that
radiation sometimes behaves as particle nature and sometimes as wave and both cannot be
separated.It can also be understood that both particle and wave properties of radiation cannot
appear simultaneously.
de-Broglie Hypothesis
In 1924, de-Broglie proposed that wave particle duality is not only associated with radiation,
butmatter such as electron, proton, neutron, etc.
also possessthis dualism characteristic.
Therefore, a wave is always associated with the moving particle whether it is matter or radiation
and controls the particle. He suggested that if electromagnetic radiation can act as a particle at
some time and a wave at other time, then matter should also behave as particle at some time and
wave at other. However, there was no experimental proof at that time and the hypothesis was
totally theoretical and was simply based on the fact that nature loves symmetry. The occurrence
of properties of wave or particle depends upon the conditions under which the particular
phenomenon takes place. But remember both particle and wave cannot appear together.
According to de-Broglie hypothesis, a particle in motion always has a wave associated
with it and the motion of the particle is guided by that wave.These waves are called de-Broglie
waves or matter waves.The wavelength  of matter waves associated with a moving particle is
given by

h
h


p mv
h
(1)
2mK
wherepis the momentum, m is the mass, v is velocity and Kis the kinetic energy of the particle.
This relation is true when v<<c. However, when v is comparable to c then relativistic effects
come into the picture and hence we cannot take m as the rest mass of the particle, but it will be
the relativistic mass and will be given as
m
m0
1  (v 2 / c 2 )
So, Eq. (1) will take the form
h h 1  (v 2 / c 2 )
 
p
m0v
wherem0is the rest mass and cis the velocity of light.
(2)