How is De Broglie's hypothesis related to Bohr's atomic model? - Quora
Matter waves are a central part of the theory of quantum mechanics, being an example of The de Broglie wavelength is the wavelength, λ, associated with a massive particle and is related to its momentum, p, .. This hypothesis contained two important new features in comparison with that of Bohr, Kramers and Slater. de Broglie reasoned in that matter also can exhibit this wave-particle duality . de Broglie's equation offers a justification for Bohr's assumption (2). Bohr's quantization assumption, it also demonstrates a deficiency of Bohr's model. Bohr's Quantum Theory and De Broglie Waves Broglie waves. The above Einstein's relations are therefore called Einstein - de Broglie's relations as well.
In that formula the angular velocity may be expressed by the frequency according to the relation so that the equation may be written as 26 In addition, the relation for the dipole-momentum has to be regarded: The latter one does not at all appear within the CEDM. Within the CEDM, the emission is assumed occurring equally in all directions, that which is probably not the case within the Bohr-model when a singular atom is considered.
From Bohr's Atom to Electron Waves
The Hertz-model originally relates to a spark inductor and not to a rotating dipole as it would be the case e. Therefore, an application of the hitherto customary model of the Hertz-oscillator onto the Bohr-model seems being not admissible. An obvious approach for expressing these properties is a formal one, applying a differential equation which reveals that the decrease of the potential energy must be equal to the increase of the kinetic energy while the total energy remains constant, i.
In particular, the temporal course of the radius r as well as that one of the velocity u is not known, the latter one being composed of different kinds of velocities whose correlations are not simply evident.
So it seems necessary starting from a vivid model implying some plausible assumptions and applying physically correct relations which must lead to consistent results. A considerable handicap is thereby the fact that it is not possible to construct an adequate macro physical model.
Matter wave - Wikipedia
The unique empirical proof is given by the discrete spectres, while the correlation to the Bohr model emerges from the assumption that it solely represents a limiting case of the vibration or oscillation process in the atom, namely characterized by the top position of the electron where the oscillation rate is zero.
Since that excitation takes place perpendicularly to the rotation plane, the orbital angular momentum of the ground state must remain constant also in the excited states, according to the theorem of constant orbital momentum. This assumption is of great importance for the whole theory. At first it seems peculiar considering the fact that, according to equation 2the Bohr model implies an n-fold magnitude of the orbital momentum in the excited states.
Therefore, the following relation shall be valid: Electrons move in circular orbits that are at fixed distances from the nucleus. However, it failed to explain the electronic structure in atoms that contained more than one electron. While some physicists initially tried to adapt Bohr's model to make it useful for more complicated systems, they eventually concluded that a completely different model was needed.
Wave-particle duality and the de Broglie wavelength Another major development in quantum mechanics was pioneered by French physicist Louis de Broglie.
Based on work by Planck and Einstein that showed how light waves could exhibit particle-like propertiesde Broglie hypothesized that particles could also have wavelike properties. What are wavelike properties?
- Matter wave
- The quantum mechanical model of the atom
Examples of observable wavelike behavior are interference and diffraction. For example, when light is shined through a barrier with two slits, as in Young's double-slit experimentthe light waves will diffract through the slits.
The destructive and constructive interference between the light waves produces a pattern of dark and light areas on the detector. De Broglie derived the following equation for the wavelength of a particle of mass m. It was also good evidence that Bohr's theory was close to correct for the innermost electrons in the atom, those in the field of the unshielded nucleus. The appearance of this factor was not understood at the time, because it was thought that there were more electrons in the innermost shell.
Bohr later remarked that Moseley's extremely clear x-ray work had far more impact than Rutherford's scattering experiment in widening acceptance of the Bohr-Rutherford atom.
Tragically, Moseley died two years later, killed by a bullet in the head at Gallipoli. What the Bohr model did do was to tie together previously unrelated phenomena, and therefore clarify the agenda for future investigations.
It showed there was a link between the Balmer formula, Planck's constant and the nuclear atom, with quantized angular momentum playing a central role. On the other hand, despite heroic efforts over several years by Bohr and others, there was no successful prediction of the observed spectral lines for the next simplest atom — neutral helium.
Evidently, to make further progress in understanding atoms, some new insight was needed.