The History of the Atomic Model: Schrodinger and the Wave Equation


Erwin Schrodinger as well as being famous for his cats in radioactive boxes was a driving force behind the treatment of electrons as both waves and particles and the treatment of electrons using quantum mechanics, a field of science that delved deeper into the mathematics and theory of sub atomic particles.

The model of the electron in the nucleus was further developed by the work of Erwin Schrodinger and his development of his wave equation. This equation could be used to solve and give an accurate description of the energy of an electron in an atom due to vibrational modes and the creation of peaks and troughs when these electrons are treated as waves.

Erwin Schrodinger was important in the driving of a mathematical and quantum mechanics  for developing the understanding of electrons in moving away from the Bohr Model. In the Bohr Model the electron is treated as a particle in fixed orbits around the nucleus where as Schrodinger’s model treated the electron as a wave that occupies three dimensional space. This expanded the understanding of the electron to have 4 quantum numbers. The quantum numbers of an electron give it its own identity and these combined are described by a wave function that obeys the Schrodinger equation. Each electron has its own unique 4 quantum numbers as according to the Pauli exclusion principle no two electrons can share the same combination of quantum numbers.

The 4 quantum numbers are:

  1. Orbital angular momentum (l) – Describes the shape of the orbital.
  2. The principal quantum number (n) - describes the energy of the electron and its distance from the nucleus.
  3. The magnetic quantum number (ml) – describes the energy level in the subshell
  4. The electron spin number (ms) -describes the spin of the electron either up or down

Schrodinger’s theory made use of electrons as waves, treating them as clouds of negative charge. Schrodinger’s equation mathematically determined the regions that an electron was most likely to be found in the orbital lobes.

Terms in section
Erwin Schrodinger

Erwin Schrodinger was an Austrian physicist who used mathematical models to enhance the Bohr model of the electron and created an equation to predicted the likelihood of finding an electron in a given position.

Vibrational Modes

Vibrational modes is a term used to describe the constant motion in a molecule. Usually these are vibrations, rotations and translations.


A peak is the highest point on a transverse wave.


A trough is the lowest point on a transverse wave.

Quantum Mechanics

The term quantum mechanics refers to energy levels and the theoretical area of physics and chemistry where mathematics is used to explain the behaviour of subatomic particles.

Bohr Model

The Bohr model refers to the treatment of electrons as particles that orbit the nucleus.

Quantum Numbers

Quantum numbers is a term used to describe the assigning of numbers to electrons as a mathematical function to describe their momentum and energy.

Pauli Exclusion principle

The Pauli Exclusion refers to the theory that each electron can only have a unique set of the 4 quantum numbers and no two electrons can have the same quantum numbers


Lobes refers to the shape of electron waves and the area of highest probability of where that electron as a particle would be found.


The History of the Atomic Model: Heisenberg’s uncertainty principle


Physical Properties of Elements