Definitions [1]
Definition: Matter Waves
According to de-Broglie, all material particles in motion have wave nature. The waves associated with moving particles of matter are called ‘de-Broglie waves' or 'matter waves'.
Formulae [2]
Formula: de-Broglie Wavelength of Electron
λ = \[\frac {12.27}{\sqrt {V}}\]Å = \[\sqrt{\frac{150}{V}}\]Å
Formula: de Broglie Wavelength
λ = \[\frac {h}{p}\]
OR
λ = \[\frac {h}{mv}\]
Key Points
Key Points: de-Broglie Wavelength
- de Broglie proposed that moving material particles have an associated wave nature, analogous to that of photons.
- The wavelength decreases with an increase in momentum or mass, and increases when the particle’s velocity decreases.
- Matter waves exist only for moving particles and are independent of whether the particle is charged or uncharged, showing they are not electromagnetic in nature.
Key Points: Particle Nature of Radiation
- Interference, diffraction, and polarisation are explained by the wave nature of radiation, whereas the photoelectric and Compton effects require the particle (photon) nature of radiation.
- Radiation exhibits dual behaviour, behaving as a wave or a particle depending on the experimental context.
- Planck (1900) proposed that radiation is emitted in discrete packets of energy, now known as photons.
- Each photon has definite energy E = hν and momentum p = \[\frac {hν}{c}\], moving with the speed of light.
- A photon has zero rest mass, but has kinetic (equivalent) mass \[\frac {hv}{c^2}\].
- For a given frequency, all photons have the same energy and momentum, irrespective of intensity.
- In photon–particle collisions, energy and momentum are conserved, and photons may be absorbed or newly created.
Key Points: Davisson–Germer Experiment (Electron Diffraction)
- Davisson and Germer (1927) experimentally demonstrated electron diffraction, confirming the wave nature of electrons.
- In the experiment, electrons accelerated by a potential difference are directed onto a nickel crystal, and the diffracted electrons are detected using a Faraday cylinder.
- A prominent intensity peak (bump) is observed for electrons accelerated through 54 V, indicating diffraction.
- The wavelength calculated using the de Broglie hypothesis matches closely with the wavelength obtained from Bragg’s diffraction condition.
- The experiment directly verifies de Broglie’s hypothesis, demonstrating that moving particles exhibit wave-like behaviour.
