Equations de Broglie

The momentum of a particle is the product of its mass and speed, p = mu. Making this substitution and solving for A gives a form of the de Broglie equation that links the wavelength of a particle with its mass and speed ... 

The de Broglie equation predicts that eveiy particle has wave characteristics. The wave properties of subatomic particles such as electrons and neutrons play important roles in their behavior, but larger particles such as Ping-Pong balls or automobiles do not behave like waves. The reason is the scale of the waves. For all except subatomic particles, the wavelengths involved are so short that we are unable to detect the wave properties. Example illustrates this. 

This problem deals with particle-waves that have mass. Equation, the de Broglie equation, relates the mass and speed of an object to its wavelength. 

The number k is more than just a simple number to designate a wave function. According to the de Broglie equation, p = h/X, every electron can be assigned a momentum p (h = Planck s constant), k and the momentum are related ... 

The behaviour of electrons in metals shows the translational properties of quantum particles having quantized energy levels. These cannot be approximated to the continuous distribution describing particles in a gas because of the much smaller mass of the electron when compared with atoms. If one gram-atom of a metal is contained in a cube of length L, the valence electrons have quantum wavelengths, X, described by the de Broglie equation... 

The de Broglie equation is X = h/mv. This means that, for a given wavelength to be... 

In the linear approximation, which was the version presented by de Broglie, equation (1) reads as... 

The de Broglie concept of wave-particle duality enables us to calculate the wavelength of an electron. According to the de Broglie equation,... 

Atomic line spectra arise because electromagnetic radiation occurs only in discrete units, or quanta. Just as light behaves in some respects like a stream of small particles (photons), so electrons and other tiny units of matter behave in some respects like waves. The wavelength of a particle of mass m traveling at a velocity v is given by the de Broglie equation, A = h/mv, where h is Planck s constant. 

We can use the de Broglie equation take the mass of an electron as 0.922 x 10-30 kg. The velocity of the electron is found by equating its kinetic energy, mv2, to the 10 keV loss of electric potential energy. 

Shortly after Bohr s proposal, Louis de Broglie made an important proposal. He said that if waves have matter-like properties, then matter should have wave-like properties. It is not necessary for you to know the de Broglie equation, but you should understand that it predicted that matter of normal mass would create infinitesimally small waves. It is only matter with an extremely small mass, like an electron, and traveling at high speed that will emit appreciable wavelengths. 

Answer Using the de Broglie equation, we can substitute our given information to find the wavelength of the baseball ... 

Every particle has a wave-like character. Following the de Broglie equation, a particle of mass m moving at a velocity v is associated with a wavelength given by the equation... 

Table II. Wavelengths Associated with Various Particles Calculated from the de Broglie Equation...

Electrons moving in circles around the nucleus, as in Bohr s theory, can be thought of as forming standing waves that can be described by the de Broglie equation. However, we no longer believe that it is possible to describe the motion of an electron in an atom so precisely. This is a consequence of another fundamental principle of modern physics, Heisenberg s uncertainty principle, which states that there is a relationship... 

Dalton s atomic theory, overview, 1 De Broglie equation, 23 Delocalization energy, definition, 174 Density functional theory chemical potential, 192 computational chemistry, 189-192 density function determination, 189 exchange-correlation potential and energy relationship, 191-192 Hohenberg-Kohn theorem, 189-190 Kohn-Sham equations, 191 Weizsacker correction, 191 Determinism, concept, 4 DFT, see Density functional theory Dipole moment, molecular symmetry, 212-213... 

Problem 2.8 Considering the solution = sinfcc of Eq. (2.35) with k = 2mEy/% as a sine wave sin(27ra /A) of wavelength = 2itlk, reproduce the de Broglie equation p = hjX. 

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