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De Broglie Wavelength for Electrons

In 1924 Louis-Victor de Broglie hypothesized that if the wave length of light (Lambdalight) could be determined by the energy contained in a particle (photon) of light, according to the relation:

Lambdalight = h.c / Ephoton

then perhaps physical particles such as electons could have a wavelength determined by their energy, as well. Note that h is Planck's Constant and c is the speed of light.

To be able to compare like quantitues between electrons and photons, he recast the above expression for Lambdalight in terms of the momentum of a photon. Relativity Theory gives the momentum (p) of a photon as:

pphoton = Ephoton / c

Substituting the resulting expression for Esub>photon into the above expression for Lambdalight gives:

Lambdalight = h / pphoton

De Broglie then used this expression to calculate a wave length for an electron subsituting 'm.v' for the momentum 'p' where 'm' is the mass of the electron and 'v' is the electron velocity.

Lambdaelectron = h / (m.v)

In 1927 at Bell Labs, Clinton Davisson and Lester Germer demonstrated that electrons did indeed create a diffraction patttern consistent with their De Broglie wavelength. They did this by firing slow-moving electrons at a crystalline nickel target and then measuring the angular dependence of the density of the deflected electrons .

POSTED: Sep:21:06 :
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