SCHRÖDINGER'S ATOMIC MODEL: CHARACTERISTICS, POSTULATES - PHYSICAL - 2025

The atomic model Schrödinger was developed by Erwin Schrödinger in 1926. This proposal is known as the quantum mechanical model of the atom, and describes the wavelike behavior of the electron.

Schrödinger suggested that the movement of the electrons in the atom corresponded to the wave-particle duality, and consequently, the 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 equation of the same name to calculate the probability that an electron is in a specific position.

Characteristics of the atomic model of Schrödinger

1s, 2s, and 2p orbitals within a sodium atom.

-Describe the movement of electrons as standing waves.

-The electrons move constantly, 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 path it takes within the atom. It just establishes a probability zone to locate the electron.

-These probability areas are called atomic orbitals. The orbitals describe a translational motion around the nucleus of the atom.

-These atomic orbitals have different levels and sub-levels of energy, 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.

Electron density indicates the probability of finding an electron near the nucleus. The closer it is to the nucleus (purple zone), the more likely it is, while it will be less if it moves away from the nucleus (purple zone).

Experiment

Schrödinger's atomic model is based on the Broglie hypothesis, as well as on the previous atomic models of 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, being Albert Einstein himself endorser of his theory.

However, de Broglie theory had a shortcoming, which was that the meaning of the idea itself was not well understood: an electron can be a wave, but of what? It is then that the figure of Schrödinger appears to respond.

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.

Here are the scientific foundations of this atomic model:

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

The de Broglie hypothesis on the wave and corpuscular nature of matter can be demonstrated using Young's experiment, also known as the double slit experiment.

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

During his experimentation, Young divided the emission of a beam of light passing through a small hole through an observation chamber. This division is achieved through the use of a 0.2 millimeter 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, when placing the card horizontally, the beam was divided into two approximately equal parts. The output of the light beams was directed by a mirror.

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

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

The Schrödinger 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 the time-independent Schrödinger equation at the end of 1926, which is based on the wave functions behaving as 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 specific frequency and amplitude.

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

The time-independent Schrödinger equation is as follows:

Where:

E: 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.

The Schrödinger 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 Schrödinger's 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 and energy of an electron. Consequently, scientists recognize that the estimate of the electron's location within the atom is inaccurate.

Postulates

The postulates of Schrödinger's atomic model are as follows:

-Electrons behave as standing waves that are distributed in space according to the wave function Ψ.

-Electrons move within the atom in 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 Ψ ².

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

However, Schrödinger's atomic model does not consider the spin of electrons, nor does it consider variations in the behavior of fast electrons due to relativistic effects.

Articles of interest

De Broglie atomic model.

Chadwick's atomic model.

Heisenberg atomic model.

Perrin's atomic model.

Thomson's atomic model.

Dalton's atomic model.

Dirac Jordan atomic model.

Atomic model of Democritus.

Bohr's atomic model.

Sommerfeld atomic model.

References

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6. Wikipedia, The Free Encyclopedia (2018). Schrödinger equation. Recovered from: es.wikipedia.org
7. Wikipedia, The Free Encyclopedia (2017). Young's experiment. Recovered from: es.wikipedia.org