**The waves associated with moving particle is called matter waves or de-Broglie wave and it propagates in the form of wave packets with group velocity.**

de-broglie-wavelength

According to de-Broglie theory, the wavelength of de-Broglie wave is given by De-Broglie wavelength, λ=h/mv; where h = Plank's constant, m = Mass of the particle, v = Speed of the particle.

- The smallest wavelength whose measurement is possible is that of γ-rays.
- The wavelength of matter waves associated with the microscopic particles like electron, proton, neutron,α-particle etc. is of the order of m.

De-Broglie wavelength associated with the charged particles

The

**energy of a charged particle**accelerated through potential difference V is
E = 1/2 mv

^{2}= q(pd)
Hence De-Broglie wavelength

De-Broglie wavelength associated with uncharged particles

For

**Neutron**De-Broglie wavelength is given as
Å

Energy of thermal neutrons at ordinary temperature 3/2kT; where k = Boltzman's constant = 1.38 x 10

^{-23}Joules/kelvin, T = Absolute temp.

So Å

Some Important Graphs:

Characteristics of matter waves:

- Matter waves are not electromagnetic in nature.

- 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.

- Electron microscope works on the basis of de-Broglie waves.

- The phase velocity of the matter waves can be greater than the speed of the light.

- The number of de-Broglie waves associated with n
^{th}orbital electron is n.

- Only those circular orbits around the nucleus are stable whose circumference is integral multiple of de-Broglie wavelength associated with the orbital electron.