# Matter Waves (de-Broglie Waves)

According to de-Broglie a moving material 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.

**de-Broglie wavelength**According to de-Broglie theory, the wavelength of de-Broglie wave is given by

where

*h*= Planckâ€™s constant,*m*= mass of the particle,*v*= Speed of the particle,*E =*energy of the particle.The smallest wavelength whose measurement is possible is that of Î³ -rays.

The wavelength of matter waves associated with the microscopic particles like electron, proton, neutron, Î±-particle etc. is of the order of 10

^{â€“10 }m.**de-Broglie wavelength associated with the charged particles**The energy of a charged particle accelerated through potential difference

*V*is

Hence, de-Broglie wavelength,

*Ã…*,

*Ã…*,

*Ã…*,

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**de-Broglie wavelength associated with uncharged particles**For neutron,

*d*e-Broglie wavelength is given as

Energy of thermal neutrons at ordinary temperature,

;

where

*T*= absolute temperature,*k*= boltzmanâ€™s constant = 1.38 Ã— 10^{â€“23}Joule/kelvin,So,

**Ratio of wavelength of photon and electron**The wavelength of a photon of energy*E*is given by*Î»*=_{ph }*hc*/*E*. While the wavelength of an electron of kinetic energy*K*is given by . Therefore, for the same energy, the ratio# Characteristics of Matter Waves

- Matter wave represents the probability of finding a particle in space.
- Matter waves are not electromagnetic in nature.
- de-Brogile or matter wave is independent of the charge on the material particle. It means matter wave of de-Broglie wave is associated with every moving particle (whether charged or uncharged).
- Practical observation of matter waves is possible only when the de-Broglie wavelength is of the order of the size of the particles.
- 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.
- Matter waves can propagate in vacuum, hence they are not mechanical waves.
- 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.