# De Broglie hypothesis

(Redirected from De Broglie wavelength)

In 1923 Louis de Broglie claimed that all matter has a wave-like nature and related its wavelength and momentum by the equation:

[itex]

\lambda = \frac{h}{p} = \frac {h}{{m}{v}} \sqrt{1 - \frac{v^2}{c^2}} [itex]

where:

[itex]\lambda[itex] is the particle's wavelength
[itex]h[itex] is Planck's constant
[itex]p[itex] is the particle's momentum
[itex]m[itex] is the particle's mass
[itex]v[itex] is the particle's velocity

The greater the energy, the larger the frequency and the shorter (smaller) the wavelength. Given the relationship between wavelength and frequency, it follows that short wavelengths are more energetic than long wavelengths.

In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow moving electrons at a crystalline Nickel target. The angular dependence of the reflected electron intensity was measured, and was determined to have the same diffraction pattern as those predicted by Bragg for X-Rays. Before the acceptance of the De Broglie hypothesis, diffraction was a property that was only exhibited by waves. Therefore, the presence of any diffraction effects by matter, demonstrated the wave-like nature of matter. When the De Broglie wavelength was inserted into the Bragg condition, the observed diffraction pattern was predicted, thereby experimentally confirming the De Broglie hypothesis.

This was a pivotal result in the development of quantum mechanics. Just as Arthur Compton demostrated the particle nature of light, the Davisson-Germer experiment showed the wave-nature of matter, and competed the theory of wave-particle duality. For physicists this idea was important because it means that not only can any particle exhibit wave characteristics, but that one can use wave equations to describe phenomena in matter if one uses the de Broglie wavelength.

Note: in French "de Broglie" is pronounced , which sounds close to "de Broy". This is an alteration of the italian pronunciation of "gl" (sound like "ll"); the original name was "Broglia", and was francisized in 1654  (http://genealogy.euweb.cz/broglie/broglie3.html).

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