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Atomic de Broglie model

Later, de Broglie statements were experimentally demonstrated by scientists Clinton Davisson and Lester Germer in 1927. De Broglie’s electron wave theory is based on Einstein’s proposal on the wave properties of light at short wavelengths.

Broglie announced the possibility that matter had a behavior similar to that of light, and suggested similar properties in subatomic particles such as electrons.

 

Characteristics of the de Broglie atomic model

To develop his proposal, Broglie started from the principle that electrons had a dual nature between wave and particle, similar to light.

In this sense, Broglie made a simile between both phenomena, and based on the equations developed by Einstein for the study of the wave nature of light, he indicated the following:

– The total energy of the photon and, consequently, the total energy of the electron, results from the product of the wave frequency and Plank’s constant (6.62606957 (29) × 10 -34 Jules x seconds), as shown detailed in the following expression:

Atomic de Broglie model

In this expression:

E = energy of the electron.

h = Plank’s constant.

f = frequency of the wave.

– The linear momentum of the photon, and therefore, of the electron, is inversely proportional to the wavelength, and both magnitudes are related through Plank’s constant:

Atomic de Broglie model

In this expression:

p = momentum of the electron.

h = Plank’s constant.

λ = wavelength.

– The linear momentum is the product of the mass of the particle and the speed that the particle has during its displacement.

Atomic de Broglie model

In this expression:

λ = wavelength.

h = Plank’s constant.

m = mass of the electron.

v = velocity of the electron.

Since h, Plank’s constant, has a small value, so is the wavelength λ. Consequently, it is feasible to state that the wave properties of the electron occur only at atomic and subatomic levels.

– Broglie is also based on the postulates of Bohr’s atomic model. According to the latter, the orbits of the electrons are limited and can only be multiples of whole numbers. A) Yes:

Atomic de Broglie model

Where:

λ = wavelength.

h = Plank’s constant.

m = mass of the electron.

v = velocity of the electron.

r = radius of the orbit.

n = integer.

According to Bohr’s atomic model, which Broglie adopted as a basis, if electrons behave like standing waves, the only orbits allowed are those whose radius is equal to an integer multiple of the wavelength λ.

Therefore, not all orbits meet the necessary parameters for an electron to move through them. This is why electrons can only move in specific orbits.

The de Broglie electron wave theory justified the success of Bohr’s atomic model in explaining the behavior of the single electron of the hydrogen atom.

Similarly, it also shed light on why this model did not fit more complex systems, that is, atoms with more than one electron.

Davisson and Germer experiment

The experimental verification of the de Broglie atomic model took place 3 years after its publication, in 1927.

The prominent American physicists Clinton J. Davisson and Lester Germer experimentally confirmed the theory of wave mechanics.

Davisson and Germer carried out scattering tests of an electron beam through a nickel crystal and observed the phenomenon of diffraction through the metallic medium.

The experiment carried out consisted of carrying out the following procedure:

– In the first instance, an electron beam assembly was placed that had a known initial energy.

– A voltage source was installed to accelerate the movement of electrons by inciting a potential difference.

– The flow of the electron beam was directed towards a metallic crystal; in this case, nickel.

– The number of electrons that impacted on the nickel crystal was measured.

At the end of the experimentation, Davisson and Germer detected that the electrons scattered in different directions.

By repeating the experiment using metallic crystals with different orientations, the scientists detected the following:

– The scattering of the electron beam through the metallic crystal was comparable to the phenomenon of interference and diffraction of light rays.

– The reflection of the electrons on the impact crystal described the trajectory that, theoretically, it should describe according to the de Broglie electron wave theory.

In short, the Davisson and Germer experiment experimentally verified the dual wave-particle nature of electrons.

Limitations

The de Broglie atomic model does not predict the exact location of the electron on the orbit in which it travels.

In this model, electrons are perceived as waves that move throughout the orbit without a specific location, thereby introducing the concept of an electronic orbital.

Atomic de Broglie model

Furthermore, the de Broglie atomic model, analogous to the Schrödinger model, does not consider the rotation of the electrons on the same axis ( spin ).

By ignoring the intrinsic angular momentum of electrons, the spatial variations of these subatomic particles are being neglected.

In the same vein, this model also does not take into account the changes in the behavior of fast electrons as a consequence of relativistic effects.

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