Talha's Physics Academy
De Broglie Hypothesis and Davisson-Germer Experiment
De Broglie Hypothesis
It has been observed that light displays a dual nature; it behaves as a wave and it acts as a particle. Assuming symmetry in nature, the French physicist Louis de Broglie proposed in 1924 that particles of matter should also possess a wave-like nature.
As the momentum $p$ of a photon is given by the relation:
Rearranging this for wavelength $\lambda$:
For a particle of mass $m$ moving with velocity $v$, its momentum is $p = mv$. Therefore:
The above expression is known as the De Broglie Wavelength.
Davisson and Germer Experiment
The experimental setup designed by Davisson and Germer was enclosed in a vacuum chamber. A beam of electrons, accelerated through a known potential $V$, was allowed to strike a nickel crystal. Measurements were made to count the number of electrons scattered by the crystal at various angles.
Observations
Davisson and Germer reported unexpected results: the electrons reflected very strongly at certain angles only and not in other directions, behaving similarly to X-ray diffraction patterns.
They further investigated properly oriented crystals to observe if it could be possible to interpret that electrons behave as waves of all wavelengths ($\lambda$) as given by De Broglie's hypothesis. They calculated the wavelength of an electron from the known accelerating potential $V$ by applying the kinetic energy relation:
$v = \sqrt{\frac{2Ve}{m}}$
According to the De Broglie hypothesis:
Putting the value of velocity $v$ into the above equation:
$\lambda = \frac{h}{\sqrt{2mVe}}$
The wavelength associated with the above equation agreed perfectly with De Broglie's prediction. Thus, it was confirmed experimentally that an electron has a wave-like nature, because only a wave exhibits wavelength and diffraction properties.
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