Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. De Broglie derived his equation using well established theories through the following series of substitutions: De Broglie first used Einstein's famous equation relating matter and energy: Using Planck's theory which states every quantum of a wave has a discrete amount of energy given by Planck's equation: Since de Broglie believed particles and wave have the same traits, he hypothesized that the two energies would be equal: Because real particles do not travel at the speed of light, De Broglie submitted velocity (\(v\)) for the speed of light (\(c\)). Question 8: The de Broglie wavelength of a particle is the same as the wavelength of a photon. In 1927, Clinton J. Davisson and Lester H. Germer shot electron particles onto onto a nickel crystal. Microscopic particle-like electrons also proved to possess this dual nature property. Have questions or comments? Electromagnetic radiation, exhibit dual nature of a particle (having a momentum) and wave (expressed in frequency, wavelength). The de Broglie wavelength of … E = … D e Broglie Wavelength of Electron Derivation. The de Broglie equation is one of the equations that is commonly used to define the wave properties of matter. Watch the recordings here on Youtube! According to de Broglie, every moving particle sometimes acts as a wave and sometimes as a particle and vice versa. De Broglie was able to mathematically determine what the wavelength of an electron should be by connecting Albert Einstein's mass-energy equivalency equation (E = mc 2) with Planck's equation (E = hf), the wave speed equation (v = λf) and momentum in a series of substitutions. The wave associated with moving particles is the matter-wave or de Broglie wave whose wavelength is called the de Broglie wavelength. \[ \lambda = \dfrac{h}{p}= \dfrac{h}{mv} =\dfrac{6.63 \times 10^{-34}\; J \cdot s}{(9.1 \times 10^{-31} \; kg)(5.0 \times 10^6\, m/s)}= 1.46 \times 10^{-10}\;m\]. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. de-Broglie wavelength = h/√ (2×m×e×V) de-Broglie wavelength = (6.625×10-14)/√(2×9.11×10-31×1.6×10-17×400) Wavelength = 0.6135 Å. Missed the LibreFest? For an electron, de Broglie wavelength … Louis de Broglie in his thesis suggested that any moving particle, whether microscopic or macroscopic will be associated with a wav… Legal. Deriving the de Broglie Wavelength. Through the equation \(\lambda\), de Broglie substituted \( v/\lambda\) for \(\nu\) and arrived at the final expression that relates wavelength and particle with speed. What scientists discovered was the electron stream acted the same was as light proving de Broglie correct. By using a series of substitution de Broglie hypothesizes particles to hold properties of waves. De Broglie derived his equation using well established theories through the following series of substitutions: De Broglie first used Einstein's famous equation relating matter and energy: \[ E = mc^2 \label{0}\] with … What they saw was the diffraction of the electron similar to waves diffraction against crystals (x-rays). The de Broglie wavelength is the wavelength, \(\lambda\), associated with a object and is related to its momentum and mass. λ = h/mv, where λ is wavelength, h is Planck's constant, m is the mass of a particle, moving at a velocity v. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. The de Broglie equation is an equation used to describe the wave properties of matter, specifically, the wave nature of the electron : . Within a few years, de Broglie's hypothesis was tested by scientists shooting electrons and rays of lights through slits. Find the de Broglie wavelength for an electron moving at the speed of \(5.0 \times 10^6\; m/s\) (mass of an electron is \(9.1 \times 10^{-31}\; kg\)). According to wave-particle duality, the De Broglie wavelength is a wavelength manifested in all the objects in quantum mechanics which determines the probability density of finding the object at a given point of the configuration space. To derivate the de Broglie wavelength of an electron equation, let’s take the energy equation which is. Then, the photon’s energy is: (a) Equal to the kinetic energy of the particle. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. In 1923, Louis de Broglie, a French physicist, proposed a hypothesis to explain the theory of the atomic structure. It basically describes the wave nature of the electron. \[ mv^2 = \dfrac{hv}{\lambda} \label{4}\], \[ \lambda = \dfrac{hv}{mv^2} = \dfrac{h}{mv} \label{5} \], A majority of Wave-Particle Duality problems are simple plug and chug via Equation \ref{5} with some variation of canceling out units.


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