1. Satish Pradhan Dnyanasadhana college, Thane
Subject-Physics
Paper-II
Class- F. Y. B. Sc
Topic-Wave nature of particles
Presented By
Ms. Ankita P. Angre
Department of Physics

2. Wave nature of particles

3. Nature of a wave
A wave is described by frequency , wavelength , phase velocity u and intensity I
A wave is spread out and occupies a relatively large region of space

4. Nature of a particle
A particle is specified by mass m, velocity v, momentum p, and energy E
A particle occupies a definite position in space.
In order for that it must be small

5. Light
Interference and Diffraction experiments showed the wave nature of light
Blackbody radiation and Photoelectric effect can be explained only by considering light as a stream of particles

6. So is light a wave or a particle ?

7. How are they related? E = h p=h/ E– energy of the photon
– frequency of the wave
h– plank's constant
p=h/
p – momentum of the particle
 - wavelength of the photon

8. CENTRE FOR EMERGING TECHNOLOGIES
DE BROGLIE HYPOTHESIS
In the Year 1924 Louis de Broglie
made the bold suggestion
“ If radiation which is basically a wave can exhibit particle nature under certain circumstances, and since nature likes symmetry, then entities which exhibit particle nature ordinarily, should also exhibit wave nature under suitable circumstances”
The reasoning used might be paraphrased as follows
Nature loves symmetry
Therefore the two great entities, matter and energy, must be mutually symmetrical
If energy (radiant) is undulatory and/or corpuscular, matter must be corpuscular and/or undulatory
LOUIS DE BROGLIE
SRI BHAGAWAN MAHAVEER JAIN COLLEGE OF ENGINEERING

9. The de Broglie Hypothesis
If light can act like a wave sometimes and like a particle at other times, then all matter, usually thought of as particles, should exhibit wave-like behaviour
The relation between the momentum and the wavelength of a photon can be applied to material particles also
Prince Louis de Broglie ( )

10. Relates a particle-like property (p) to a wave-like property (l)
de Broglie Wavelength
Relates a particle-like property (p) to a wave-like property (l)

11. The Wave associated with the matter particle is called Matter Wave.
DE BROGLIE WAVELENGTH
The Wave associated with the matter particle is called Matter Wave.
The Wavelength associated is called de Broglie Wavelength.

12. The frequency
De Broglie postulated that all particles satisfy Einstein’s relation
In other words,

13. Example: de Broglie wavelength of an electron
Mass = 9.11 x kg Speed = 106 m / sec
This wavelength is in the region of X-rays

14. Example: de Broglie wavelength of a ball
Mass = 1 kg Speed = 1 m / sec

15. Theoretical implication – The Bohr postulate
Consider standing waves produced in a stretched string tied at two ends
Condition for these standing waves is that the length of the string should be integral multiple of /2

16. Bragg Scattering
Bragg scattering is used to determine the structure of the atoms in a crystal from the spacing between the spots on a diffraction pattern (above)

17. The Diffraction
X-rays
electrons
The diffraction patterns are similar because electrons have similar wavelengths to X-rays

18. Wave-like Behaviour of Matter
Evidence:
electron diffraction
electron interference (double-slit experiment)
Also possible with more massive particles, such as neutrons and a-particles
Applications:
Bragg scattering
Electron microscopes
Electron- and proton-beam lithography

19. Wave-Particle Duality
wave function

20. Wave Function
Completely describes all the properties of a given particle
Called y = y (x,t); is a complex function of position x and time t

21. Wave-Particle Duality
wave function

22. PHASE VELOCITY
Phase velocity: The velocity with which a wave travels is called Phase velocity or wave velocity. It is denoted by vp. It is given by
Where c = velocity of light and v = is velocity of the particle.
The above equation gives the relationship between the phase velocity and
particle velocity.
It is clear from the above equation that, Phase velocity is not only greater than the velocity of the particle but also greater than the velocity of light,
which can never happen. Therefore phase velocity has no physical
meaning in case of matter waves. Thus a concept of group velocity was
introduced.

23. GROUP VELOCITY
Since phase velocity has no meaning, the concept of group velocity was introduced as follows.
“ Matter wave is regarded as the resultant of the superposition of large number of component waves all traveling with different velocities. The resultant is in the form of a packet called wave packet or wave group. The velocity with which this wave group travels is called group velocity.” The group velocity is represented by vg. Vg
Particle Vp

24. Thank you