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# Investigate de Broglie’s matter waves

By the 19th century it was firmly established that light behaved like a wave and matter behaved like a particle.

In the 20th century it was discovered that light can behave as quantized particles also.

Thus to explain Bohr’s quantization of electron orbits, Louis de Broglie in 1923 suggested that perhaps electrons and matter in general exhibit wavelike properties and have wavelength associated with it.

- de Broglie suggested that the wavelength of a particle , is related to its momentum
*p*, according to the equation :*h*= Planck’s constant [6.63 x 10^{-34 }*Js*]

- According to this equation , the wavelength of a tennis ball of mass 0.05kg, moving at a speed of 50ms
^{-1}, would be- This is an extremely short wavelength.
- This accommodates for the fact that we don’t generally observe matter exhibit wavelike properties like diffraction, refraction or interference.

- However for an extremely small particle such as electrons, the calculations of wavelength would give us:
*m*= 9.1 x 10_{e}^{-31}*kg*- under suitable conditions, electrons can be accelerated to speed of :
*v*= 6.0 x 10^{6}*m*s^{-1} - Thus ,
- Although this is a small number, it is in the same order of magnitude as the interatomic spacing in crystals.

- Thus electrons could be diffracted through the atomic structure of the crystal , and if electrons behaved as waves, it would show diffraction patterns.
- This allowed physicists to test for evidence of de Broglie’s matter waves.

- 1927 Davisson and Garner directed a beam of electrons at a metal crystal
- The openings between the atoms in the crystal lattice could be used as a diffraction grating.
- The electrons after scattering through the crystal lattice were detected at regular peaks.
- When the angle and distance between these peaks from the diffraction pattern were measured, and the wavelength , it was found to match the wavelength calculated theoretically by de Broglie’s hypothesis.
- de Broglie proposed that as a wave, electrons would only be in stable orbits if there is constructive interference, the electron formed a standing wave in that orbit.
- This meant that the circumference had to be an integral multiple of the wavelength.

Extract from *Physics Stage 6 Syllabus *© 2017 NSW Education Standards Authority (NESA)