## NEET Physics Notes Optics- Matter Waves de-Broglie Waves

**de-Broglie Waves**

The concept of de-Broglie waves reflects the wave-particle duality of matter. The waves associated with moving matter particles are called matter waves or de-Broglie waves.

The de-Broglie relations shows that the wavelength is inversely proportional to the momentum of a particle and is also called de-Broglie wavelength. Also, the frequency of matter waves is directly proportional to the total energy E of a particle.

The wavelength of de-Broglie waves is given by the relation

where, K is the kinetic energy of moving particle.

The smallest wavelengths whose measurement is possible is that of y-rays. The wavelength of matter waves associated with the microscopic particles like electron, proton, neutron etc., is of the order of lCT10m.

Matter wave represents the probability of finding a particle in space. Matter wave propagates in the form of wave packets with its group velocity.

Electron microscope works on the basis of de-Broglie wave. Concept of matter waves was experimentally verified by experiments like

- Davisson and Germer experiment,
- GP Thomson’s diffraction experiment for electron waves
- .
**Note** - Matter waves are independent of the charge on the material particle.
- The phase velocity of the matter waves can be greater than the speed of light. Matter waves can propagate in vacuum, hence they are not mechanical waves.
- For smaller particles we are using quantum mechanics which takes into account the dual nature.

**Matter Waves Associated with Charged Particles**

If a charged particle of mass m and charge q is accelerated through a potential difference V, then

**Matter Wave Associated with Neutrons**

If we have a thermal neutron particle of energy K, then

, where k is **Boltzmann’s constant** and T is the **absolute temperature**. Hence,

**Davisson-Germer Experiment**

- The de-Broglie hypothesis was confirmed by Davisson-Germer experiment. It is used to study the scattering of electron from a solid or to verify the waves nature of electron.
- A beam of electrons emitted by electron gun is made to fall on nickel crystal cut along cubical axis at a particular angle. Ni crystal behaves like a three dimensional diffraction grating and it diffracts the electron beam obtained from electron gun.
- The diffracted beam of electrons is received by the detector which can be positioned at any angle by rotating it about the point of incidence.
- The energy of the incident beam of electrons can also be varied by changing the applied voltage to the electron gun.
- According to classical physics, the intensity of scattered beam of electrons at all scattering angle will be same but Davisson and Germer found that the intensity of scattered beam of electrons was not same but different at different angles of scattering.
- It is maximum for diffracting angle 50° at 54 V potential difference.

If the de-Broglie waves exist for electrons, then these should be diffracted as X-rays. Using the Bragg’s formula we can determine the wavelength of these waves, where d = distance

between diffracting planesglancing angle for incident beam = Bragg’s angle. Clearly from figure, we have