Modern Physics

# Schrödinger’s atomic model: characteristics, postulates

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

For this, the prominent Austrian physicist based himself on the hypothesis of Broglie, who stated that each particle in motion is associated with a wave and can behave as such.

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

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

## Characteristics of the Schrödinger Atomic Model

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

-Describe the movement of electrons as standing waves.

-The electrons move constantly, that is, they don’t have a fixed or defined position inside the atom.

-This model does not predict the location of the electron, nor does it describe the route it takes inside the atom. Establish just one probability zone to locate the electron.

-These areas of probability are called atomic orbitals. Orbitals describe a translational 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 include the stability of the nucleus, it only refers to the explanation of quantum mechanics associated with the movement of electrons inside the atom.

## Experience

Schrödinger’s atomic model is based on Broglie’s hypothesis and on the earlier atomic models of Bohr and Sommerfeld.

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

The following are the scientific foundations of this atomic model:

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

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

English scientist Thomas Young laid the foundations for Schrödinger’s atomic model when, in 1801, he conducted the experiment to verify the nature of light waves.

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

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

The two beams of light hit a wall in a dark room. There was evidence of the interference pattern between the two waves, which showed that light could behave as much as a particle as a wave.

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

### Schrodinger’s Equation

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

For atomic analysis, Schrödinger published in late 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 certain frequency and amplitude.

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

Schrödinger’s time-independent equation is as follows: Where:

E : constant 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, is not time dependent. However, the function that describes the total wave motion will always depend on time.

The Schrödinger equation indicates that, if there is a functional wavefunction, and the Hamiltonian operator acts on it, the proportionality constant E represents the total energy of the quantum system in one of its steady states.

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

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

According to the Heisenberg uncertainty principle, it is not possible to estimate the position or energy of an electron. Consequently, scientists recognize that the estimate of the electron’s location in the atom is imprecise.

## postulates

The postulates of the Schrödinger atomic model are as follows:

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

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-The electrons move inside the atom in the description of the orbitals. These are areas where the probability of finding an electron is considerably higher. The referred probability is proportional to the square of the Ψ 2 wave function .

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 electron rotation, nor does it consider variations in the behavior of fast electrons due to relativistic effects.