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What is Sommerfeld’s atomic model?

Sommerfeld atomic model

Arnold Sommerfeld was a famous atomic mathematician and physicist known primarily for his work on atomic theory in the field of quantum mechanics and for mentoring more Nobel Laureates in physics than any other physicist. Sommerfeld discovered that in some atoms, electrons managed to reach speeds very close to the speed of light, so he chose to base his analysis on relativistic theory . This decision was full of intrigue and controversy at the time, because the theory of relativity had not yet been accepted in the scientific community.

Sommerfeld atomic model

What is Sommerfeld’s atomic model?

The atomic model Sommerfeld is a better version of the model Bohr , which explains the way in which they behave electrons through different levels of energy that exist within the atom giving rise to the modeling of the atom.

  • What is the Sommerfeld atomic model?
  • features
  • Sommerfeld atomic model postulates
  • Contributions
  • What problems does Sommerfeld’s atomic model present?
  • Importance

What is the Sommerfeld atomic model?

Sommerfeld’s atomic model consists of explaining the behavior of electrons , stating that within the same energy level there could be different energy sublevels , which caused different energy variations to occur at the same level. He also explained that the speeds of electrons were close to the speed of light, which is why he studied electrons from a relativistic perspective .

He made two basic modifications, one was that electrons could describe quasi-elliptical orbits , and the other was that electrons had relativistic speeds . According to his model, the electrons were spinning only in a circular fashion . A centric orbit gave rise to a new quantum number which was called Azimuthal quantum number , and which would delimit the shape of the orbitals, and would be represented by the letter l, taking variable values ​​from 0 to n-1.

In this way the orbits according to Sommerfeld’s atomic model are:

  • l = 0 would be those that would later be known as S orbitals.
  • l = 1 would be called 2p orbital or principal orbital .
  • l = 2 would be known as d, u fuzzy orbital .
  • L = 3 would be the orbital called fo fundamental .

features

The main characteristics of Sommerfeld’s atomic model are the following:

  • He looked for a way to perfect Bohr’s atomic model by making some modifications .
  • He postulated that the nucleus of the atom was not immobile but, on the contrary, could move in the center of the system.
  • It was proposed in the model that the orbits of the electron could be circular and elliptical .
  • It was introduced in secondary quantum number better known as azimuthal .
  • It is regarded as a generalization of the Bohr model .
  • In his model, the electrons were in circular orbits around the nucleus, without radiating any type of energy.
  • Only orbits were enabled where the angular momentum of the electron met certain characteristics.
  • The energy released when an electron descends from one orbit to another was produced in the form of light energy .

Sommerfeld atomic model postulates

This model postulates the following:

  • Within the same energy level (n) there are sublevels
  • There are not only circular orbits but there can also be elliptical orbits that are determined by the azimuthal quantum number (l) that takes values ​​from 0 to n-1:
    • l = 0 → form the s orbital
    • l = 1 → forms the p orbital
    • l = 2 → forms the d orbital
    • l = 3 → form the f orbital
  • Adapt Bohr’s model to relativistic mechanics since electrons move at speeds close to those of light.
  • For Sommerfeld, the electron is an electric current .

Contributions

Sommerfeld’s main contribution was to conclude the difference of energy that exists between the electrons , regardless of whether they were in the same energy level was caused to the existence of energy sublevels within each level.

Sommerfeld relied on Coulomb’s Law to ensure that if an electron was subjected to a force inversely proportional to the square of the distance, the trajectory described should be elliptical and that it did not always have to be circular .

He used Einstein’s theory of relativity to treat electrons differently, and thus be able to evaluate their behavior based on the speeds reached by these fundamental particles.

What problems does Sommerfeld’s atomic model present?

The main problem with Sommerfeld’s atomic model was that it took a particle with a certain trajectory around the nucleus , however, the proper conception of the trajectory of the electrons in the atom is obsolete. Furthermore, the model failed to explain the emission form of elliptical orbits , and only worked with circular orbits .

Importance

Sommerfeld made important contributions to the mathematical theory of diffraction . His most important contribution is considered to have been his atomic model . In 1915, Sommerfeld considered the existence of elliptical orbits in addition to the circular orbits of the Bohr model and took into consideration that electrons in some atoms could move at relativistic speeds .

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