De Broglie hypothesis

u can share this

1. EAST WEST UNIVERSITY Group Member: Sudeb Das ID:2014-2-55-023 Susmita Sarkar ID: Ayan Chowdhury ID:2016-1-50-016 Presentation: De Broglie Hypothesis

2. Background The non-particle behavior of matter was first proposed in 1923, by  Louis de Broglie , a French physicist. In his PhD thesis, he proposed that particles also have wave-like properties. Although he did not have the ability to test this hypothesis at the time, he derived an equation to prove it using Einstein's famous mass-energy relation and the Planck equation.

3. Introduction De Broglie Hypothesis: In quantum mechanics, any object can behave both like wave-particle duality at the sub-microscopic level.  Wave-particle Duality: An object can act as both wave and particle at a same time. This phenomenon is called wave-particle duality. So, the object would have energy packets, momentum(can be passed to another object ), wave length, frequency and amplitude etc. By using photo-electric effect and C ompton effect we can easily describe about the wave particle duality

4. A beam of light can be treated as a stream of particles (PHOTONS) with zero rest mass Each photon has energy: where h is a constant (Planck’s constant, h ≈ 6.63 x 10 -34 Js) f, λ , c, are frequency, wavelength and velocity of light (in vacuum) respectively. Light intensity is proportional to PHOTON FLUX (no of photons passing through unit area per second) Einstein’s Postulate

5. consequently, particle with zero rest mass (eg photon) has momentum p given by: From Special Theory of Relativity

6. Photo-electric effect: When light of particular of a particular frequency hits on a metal plate in a vacuum, it emits charged particles which is shown to be electrons. Actual results : Maximum KE of ejected electrons is independent of intensity, but dependent on ν . For ν < ν (i.e. for frequencies below a cut-off frequency) no electrons are emitted. There is no time lag. However, rate of ejection of electrons depends on light intensity. The maximum KE of an emitted electron is then

7. Energy and frequency Also have relation between momentum and wavelength Relation between particle and wave properties of light Relativistic formula relating energy and momentum For light and Also commonly write these as angular frequency Wave vector hbar Summary of Photon Properties

8. Compton (1923) measured intensity of scattered X-rays from solid target, as function of wavelength for different angles. Result: peak in scattered radiation shifts to longer wavelength than source. Amount depends on θ (but not on the target material). Compton Effect

9. Conservation of energy Conservation of momentum From this Compton derived the change in wavelength: θ Before After Electron Incoming photon scattered photon scattered electron Compton Scattering:

10. Note that, at all angles there is also an unshifted peak. This comes from a collision between the X-ray photon and the nucleus of the atom since > > Compton Scattering:

11. Application Although it is difficult to draw a line separating wave–particle duality from the rest of quantum mechanics, it is nevertheless possible to list some applications of this basic idea. Wave–particle duality is exploited in electron microscopy, where the small wavelengths associated with the electron can be used to view objects much smaller than what is visible using visible light. Similarly, neutron diffraction uses neutrons with a wavelength of about 0.1 nm, the typical spacing of atoms in a solid, to determine the structure of solids. Photos are now able to show this dual nature, which may lead to new ways of examining and recording this behavior.

12. Conclusion   From the discussion we can come to a decision that a particle can exhibit wave particle duality and de Broglie has given the relation which is E= hv and p= But it has some limit.  A central concept of quantum mechanics, duality addresses the inadequacy of conventional concepts like "particle" and "wave" to meaningfully describe the behavior of quantum objects. Since. it cannot explain the Heisenberg uncertainty.