Matter waves

Review of atomic model
Davisson Geremer experiment

1. MATTER WAVES Presented By, Nagaveni G H

2. FAILURE OF CLASSICAL MECHANICS

3. CLASSICAL PHYSICS [ Pre 1900] Newtonian Mechanics Boltzmann, Gibbs…. Thermodynamics Maxwell…Electrodynamics Einstein’s General relativity and special relativity Classical chaos theory and nonlinear dynamics …………….

4. Classical mechanics is dominated by two fundamental concepts. C oncept of a particle, a discrete entity with definite position and momentum which moves in accordance with Newton's laws of motion . C oncept of an electromagnetic wave, an extended physical entity with a presence at every point in space that is provided by electric and magnetic fields which change in accordance with Maxwell's laws of electromagnetism.

5. The classical world picture is neat and tidy: the laws of particle motion account for the material world around us and the laws of electromagnetic fields account for the light waves which illuminate this world. Scientists believed that: The physical universe was deterministic. Light consisted of waves, ordinary matter was composed of particles. Physical quantities (energy, momentum, etc.) could be treated as continuous variables. There exists an objective physical reality independent of any observer.

6. We review some experimental evidences showing that several concepts of classical mechanics cannot be applied . The black-body radiation Atomic and molecular spectra The particle-like character of EMR The photoelectric effect

7. BIRTH OF

8. What happened to those ideas? T he development of quantum mechanics meant for those four “certainties” of classical physics : Classical : The physical universe is deterministic. Quantum : The physical universe is not deterministic. At the scale of atomic particles , the best that we can do is find the probability of the outcome of an experiment. We can’t predict exact results with certainty . Uncertainty is an intrinsic property of matter at this level . C lassical : Light consists of waves, while ordinary matter is composed of particles . Quantum : Both light and matter exhibit behaviour that seems characteristic of both particles and wave. ( wave-particle duality)

9. Classical : Physical quantities (energy, momentum, etc.) can be treated as continuous variables. Quantum : Under certain circumstances, some physical quantities are quantized , meaning that they can take on only certain discrete values . Classical :There exists an objective physical reality independent of any observer . Quantum : It appears that the observer always affects the experiment . It is impossible to disentangle the two.

10. REVOLUTION IN THE ATOMIC MODEL

11. DALTON’S BILLIARD BALL MODEL (1803) Recommended atoms of a particular element differ from other elements. + Atoms aren’t indivisible. -

12. THOMSON’S PLUM PUDDING MODEL [1904] Recommended Electrons as components of atom. No mention of nucleus. + -

13. RUTHERFORD’S NUCLEAR MODEL [1911] Recommended protons as components of atom; Mention of nucleus; Realized positive charge was localized in the nucleus of an atom. Do not explain why electrons remain in an orbit around the nucleus. + -

14. BOHR’S PLANETARY MODEL [1913-1924] Proposed stable electron orbits; Explained the emission spectra of some elements. Moving electron should emit energy and collapse into the nuclear model; Do not work well for Heavier atoms. + -

15. At this point in 1924, Prince Louis De-Broglie made the following observations - The whole universe is composed of matter and electromagnetic radiations. Since both are forms of energy so can be transformed to each other. The nature loves symmetry. As the radiation has dual nature, matter should also posses dual character.

16. DE-BROGLIE ‘s MATTER WAVES MODEL OF ATOM: + The waves associated with moving particle are matter waves or De-Broglie waves.

17. QUANTUM MECHANICAL (SCHRODINGER’S) MODEL OF ATOM [1926-PRESENT]

18. MATTER WAVES

19. [1924]    

20. De-Broglie wave velocity is given by,   It is assumed that the De-Broglie wave group associated with a moving particle travels with the same velocity as that of particle.

21. WAVE PACKETS: A Wave packet is a group of several waves of slightly different velocity and different wavelength.

22. Phase velocity: The velocity of component waves of a wave packet is called the Phase velocity . Group velocity: The velocity with which the wave packet obtained due to the superposition of waves travelling in a group advance is called .  

23. Group and Phase Velocity:

24. Consider two waves of same amplitude and of slightly different frequencies and wavelengths superpose and form wave packet. These waves are represented as The displacement equation of the wave packet obtained due to their superposition will be  

25. Since phase = constant, then For the amplitude of the wave packet, = constant Hence group velocity,   Phase velocity =    

26. This is the required relation between group velocity and phase velocity in dispersive medium.    

27. In a non-dispersive medium,    

28. The relationship between phase velocity, group velocity and velocity of light is given by  

29. EXPERIMENTAL EVIDENCE FOR MATTER WAVES

30. Observations made for different accelerating voltages and a number of curves are as shown in fig.

31. According to De-Broglie’s theory, the wavelength of 54V electrons is given by A˚ According to experiment, the diffracted beam at 50˚ for Nickel crystal for [111] reflecting plane d=2.15 A ˚. Applying the equation for a plane reflection grating, A˚   Experimental value is in good agreement with the theoretical value. This shows that the beam of electrons behave like X-rays suffers diffraction at reflecting surfaces and exhibits wave like properties.

32. Application of Matter Waves: Because electrons behave as waves, they can be used to “illuminate” objects in a manner similar to light. An electron microscope is an instrument that takes advantage of this situation. In electron microscopes, wavelengths as much as 100000 times smaller than those of visible light can be achieved. With such small wavelengths, electron microscopes can reveal features that are as small as 0.000000001 meters (1 nm).