Matter Waves (de-Broglie Waves)
Particle sometimes acts as a wave and sometimes as a particle.
The wave associated with moving particle is called matter wave or de-Broglie wave and it propagates in the form of wave packets with group velocity.
(1) de-Broglie wavelength:
Where h = planck’s constant, m = Mass of the particle, v = Speed of the particle, E = kinetic energy of particle.
(2) de-Broglie wavelength associated with the charged particle:
(3) de-Broglie wavelength associated with uncharged particles:
(4) Ratio of wavelength of photon and electron :
Characteristics of Matter Waves
(1) Matter wave represents the probability of finding a particle in space.
(2) Matter waves are not electromagnetic in nature.
(4) Practical observation of matter waves is possible only when the de-Broglie wavelength is of the order of size of the particles.
(5) Electron microscope works on the phenomena of de-Broglie waves.
The de-Broglie’s matter-wave concept is analogous to the Bohr’s hypothesis.