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The concept that matter behaves like a wave was proposed by French physicist Louis de Broglie (/ d ə ˈ b r ɔɪ /) in 1924, and so matter waves are also known as de Broglie waves. The de Broglie wavelength is the wavelength, λ, associated with a particle with momentum p through the Planck constant, h: =.
The de Broglie relation, [10] [11] [12] also known as de Broglie's momentum–wavelength relation, [4] generalizes the Planck relation to matter waves. Louis de Broglie argued that if particles had a wave nature, the relation E = hν would also apply to them, and postulated that particles would have a wavelength equal to λ = h / p .
On the other hand, when the thermal de Broglie wavelength is on the order of or larger than the interparticle distance, quantum effects will dominate and the gas must be treated as a Fermi gas or a Bose gas, depending on the nature of the gas particles. The critical temperature is the transition point between these two regimes, and at this ...
For de Broglie matter waves the frequency dispersion relation is non-linear: +. The equation says the matter wave frequency ω {\displaystyle \omega } in vacuum varies with wavenumber ( k = 2 π / λ {\displaystyle k=2\pi /\lambda } ) in the non-relativistic approximation.
According to the de Broglie relation, electrons with kinetic energy of 54 eV have a wavelength of 0.167 nm. The experimental outcome was 0.165 nm via Bragg's law, which closely matched the predictions. As Davisson and Germer state in their 1928 follow-up paper to their Nobel prize winning paper, "These results, including the failure of the data ...
Planck–Einstein equation and de Broglie wavelength relations P = (E/c, p) is the four-momentum, ... K max = Maximum kinetic energy of ejected electron (J)
electron thermal de Broglie wavelength, approximate average de Broglie wavelength of electrons in ... or whatever particles in a system have an average kinetic energy ...
The De Broglie relations: =, = apply. Since the potential energy is (stated to be) zero, the total energy E is equal to the kinetic energy, which has the same form as in classical physics: E = T → ℏ 2 k 2 2 m = ℏ ω {\displaystyle E=T\,\rightarrow \,{\frac {\hbar ^{2}k^{2}}{2m}}=\hbar \omega }