9 junio, 2024

Schrödinger’s atomic model: what it is, characteristics, postulates

what is the Schrödinger’s atomic model?

He Schrödinger’s atomic model it is a proposal of the functioning and structure of the atom developed by Erwin Schrödinger in 1926. It is known as the quantum mechanical model of the atom, and it describes the wave behavior of the electron.

To do this, the prominent Austrian physicist was based on the de Broglie hypothesis, who stated that each moving particle is associated with a wave and can behave as such.

Schrödinger suggested that the movement of electrons in the atom corresponded to wave-particle duality, and consequently, electrons could move around the nucleus as standing waves.

Schrödinger, who was awarded the Nobel Prize in 1933 for his contributions to atomic theory, developed the eponymous equation to calculate the probability that an electron is in a specific position.

Characteristics of the Schrödinger atomic model

-This model of the atom describes the movement of electrons as standing waves.

-The electrons are constantly moving, that is, they do not have a fixed or defined position within the atom.

-This model does not predict the location of the electron, nor does it describe the route it takes within the atom. It only establishes a probability zone to locate the electron.

-These areas of probability are called atomic orbitals. Orbitals describe a translation movement around the nucleus of the atom.

-These atomic orbitals have different energy levels and sublevels, and can be defined between electron clouds.

-The model does not contemplate the stability of the nucleus, it only refers to explaining the quantum mechanics associated with the movement of electrons within the atom.

Experiment

Schrödinger’s atomic model is based on the de Broglie hypothesis, as well as the previous atomic models by Bohr and Sommerfeld.

Broglie proposed that just as waves have properties of particles, particles have properties of waves, having an associated wavelength. Something that generated a lot of expectation at the time, with Albert Einstein himself endorsing his theory.

However, de Broglie’s theory had a shortcoming, which was that the meaning of the idea itself was not very well understood: an electron may be a wave, but of what? It is then when the figure of Schrödinger appears to give an answer.

To do this, the Austrian physicist relied on Young’s experiment, and based on his own observations, he developed the mathematical expression that bears his name.

Below are the scientific foundations of this atomic model:

Young’s experiment: the first demonstration of wave-particle duality

Broglie’s hypothesis on the wave and corpuscular nature of matter can be demonstrated by means of Young’s Experiment, also known as the double-slit experiment.

The English scientist Thomas Young laid the foundations of Schrödinger’s atomic model when in 1801 he carried out the experiment to verify the wave nature of light.

During his experimentation, Young split the emission of a beam of light passing through a small hole through an observation chamber. This division is achieved by using a 0.2 mm card, located parallel to the beam.

The design of the experiment was made so that the beam of light was wider than the card, thus, by placing the card horizontally, the beam was divided into two approximately equal parts. The output of the light beams was directed by means of a mirror.

Both beams of light hit a wall in a dark room. There, the interference pattern between the two waves was evident, thus demonstrating that light could behave both as a particle and as a wave.

A century later, Albert Einstein reinforced the idea using the principles of quantum mechanics.

Schrodinger’s equation

Schrödinger developed two mathematical models, differentiating what happens depending on whether the quantum state changes with time or not.

For atomic analysis, Schrödinger published at the end of 1926 the time-independent Schrödinger equation, which is based on the fact that wave functions behave like standing waves.

This implies that the wave does not move, its nodes, that is, its equilibrium points, serve as a pivot for the rest of the structure to move around them, describing a determined frequency and amplitude.

Schrödinger defined the waves described by electrons as stationary or orbital states, and they are associated, in turn, with different energy levels.

The time-independent Schrödinger equation is as follows:

Where:

AND: constant of proportionality.

Ψ: wave function of the quantum system.

Η ̂: Hamiltonian operator.

The time-independent Schrödinger equation is used when the observable representing the total energy of the system, known as the Hamiltonian operator, does not depend on time. However, the function that describes the total wave motion will always depend on time.

Schrödinger’s equation indicates that if we have a wave function Ψ, and the Hamiltonian operator acts on it, the constant of proportionality E represents the total energy of the quantum system in one of its stationary states.

Applied to the Schrödinger atomic model, if the electron moves in a defined space, there are discrete energy values, and if the electron moves freely in space, there are continuous energy intervals.

From the mathematical point of view, there are several solutions for the Schrödinger equation, each solution implies a different value for the constant of proportionality E.

According to the Heisenberg uncertainty principle, it is not possible to estimate the position or energy of an electron. Consequently, scientists acknowledge that the estimate of the location of the electron within the atom is inaccurate.

Postulates of the atomic model of schrödinger

The postulates of the Schrödinger atomic model are the following:

-The electrons behave like standing waves that are distributed in space according to the wave function Ψ.

-Electrons move within the atom describing orbitals. These are areas where the probability of finding an electron is considerably higher. The referred probability is proportional to the square of the wave function Ψ2.

The electronic configuration of the Schrödinguer atomic model explains the periodic properties of atoms and the bonds they form.

However, Schrödinger’s atomic model does not take into account the spin of electrons, nor does it take into account variations in the behavior of fast electrons due to relativistic effects.

Articles of interest

Broglie’s atomic model.

Chadwick’s atomic model.

Heisenberg’s atomic model.

Perrin’s atomic model.

Thomson’s atomic model.

Dalton’s atomic model.

Dirac Jordan’s atomic model.

Democritus’s atomic model.

Leucippus’ atomic model.

Bohr’s atomic model.

Sommerfeld’s atomic model.

Current atomic model.

References

The quantum mechanical model of the atom Retrieved from: es.khanacademy.org
The Schrödinger wave equation (sf). Jaime I University. Castellón, Spain. Recovered from: uji.es
Modern atomic theory: models. © ABCTE. Retrieved from: abcte.org
Schrödinger’s Atomic Model (nd). Retrieved from: erwinschrodingerbiography.weebly.com
Wikipedia, The Free Encyclopedia. Schrodinger equation. Retrieved from: es.wikipedia.org
Wikipedia, The Free Encyclopedia. Young’s experiment. Retrieved from: es.wikipedia.org

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