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It is defined by de-Broglie a moving material molecule 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.
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de-Broglie wavelength
According to de-Broglie theory, the wavelength of de-Broglie wave is given by
Where h = Plank's constant, m = Mass of the particle, v = Speed of the particle, E = Energy of the particle.
The smallest size of wavelength whose measurement is possible is that of -rays.
The wavelength of matter waves associated with the microscopic particles like electron, proton, neutron, a-particle etc. is of the range of 10-10m.
(i) de-Broglie wavelength associated with the charged particles
The energy of a charged molecule accelerated through potential energy difference V is
Hence de-Broglie wavelength 
(ii) de-Broglie wavelength associated with uncharged particles
For Neutron de-Broglie wavelength is defined as 
Energy of thermal neutrons at normal temperature
where k = Boltzman's constant = Joules/kelvin ,
T = Absolute temp.
Some graphs:
Characteristics of matter waves:
(i) Matter pulses are not electromagnetic in behavior.
(ii) Practical observation of matter waves is possible only when the de-Broglie wavelength is of the order of the size of the particles is nature.
(iii) Electron microscope works on the part of de-Broglie waves.
(iv) The medium speed of the matter waves can be greater than the speed of the light.
(v) The number of de-Broglie pulses related with nth orbital electron is n.
(vi) Only those circular orbits around the nucleus are stable whose circumference is integral multiple of de-Broglie wavelength associated with the orbital electron
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