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Schrödinger's Atomic Model, the Quantum Mechanical Model of the Atom

Schrödinger's atomic model, the quantum mechanical model of the atom

Schrödinger's atomic model was developed in 1926. It is the quantum mechanical model of the atom that started from the Schrödiger equation. In 1926, Erwin Schrödinger developed this equation to determine the probability of finding an electron at a certain point in an atom.

Until that time, electrons were only considered to rotate in circular orbits around the atomic nucleus according to Bohr's atomic model. Schrödinger claimed that electrons could also rotate in more complex elliptical orbits and calculated relativistic effects.

Solutions to the Schrödinger wave equation are also known as wave functions. The wave function gives only the probability of finding an electron at a given point around the nucleus.

What Limitations Does Bohr's Atomic Model Have?

Until 1932, the atom was believed to be composed of a positively charged nucleus surrounded by negatively charged electrons.

Bohr's model worked for the hydrogen atom. However, when the model was applied to other atoms, it was observed that electrons of the same energy level varied slightly.

This variation could not be explained in Niels Bohr's model and therefore required some correction. The proposal was that within the same energy level there were sublevels. The concrete way in which these sublevels arose naturally was by incorporating elliptical orbits and relativistic corrections.

In 1932, James Chadwick bombarded beryllium atoms with alpha particles. An unknown radiation was emitted. This particle was the neutron and its discovery brought scientists closer to a more suitable model of the atom.

What Are the Differences Between Schrödinger's and Bohr's Atomic Models?

Bohr's atomic model established an exact path for each electron within the atom. However, the quantum-mechanical model only predicts the probabilities of the position of the electron.

To solve the Schrödinger equation it is necessary to quantify the energies of the electrons. On the other hand, in Bohr's model, these quantum numbers were assumed without a mathematical basis.

 

Characteristics of the Model

Schrödinger's atomic model originally conceived of electrons as matter waves. Thus the Schrödinger equation describes the evolution in time and space of said material wave.

Later Max Born proposed a probabilistic interpretation of the wave function of electrons. However, this interpretation was a probabilistic model that allowed making empirical predictions, but in which the position and the momentum cannot be known simultaneously, due to the uncertainty principle .

This atomic model of Schrödinger can be represented as a cloud of electrons surrounding the nucleus of the atom. At the points where this cloud is densest, the probability of finding the electron is greater. Therefore, this model introduced the concept of sub-energy levels.

What Does Schrödinger's Atomic Model Predict?

Schrödinger's atomic model predicts:

  • The spectral emission lines of both neutral and ionized atoms.

  • The modification of energy levels when there is a magnetic or electric field.

  • Furthermore, with certain semi-heuristic modifications, the model explains the chemical bond and the stability of the molecules.

What Is Wrong with the Quantum Mechanical Model of the Atom?

Schrödinger's model is incomplete in the following respects:

  • It does not take into account the electronic spin.

  • The model ignores the relativistic effects of fast electrons.

  • Schrödinger's model does not explain why an electron in an excited quantum state decays to a lower level if there is a free one.

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Published: August 18, 2021
Last review: August 18, 2021