What is the magnetic quantum number in chemistry



Quantum numbers are used in quantum mechanics to describe the properties of certain particles. A set of quantum numbers completely characterizes an eigenstate of a quantum mechanical system. In contrast to the descriptive variables of classical mechanics, they can only assume discrete values. There are different quantum numbers for different properties or for different particles.

Due to their discrete nature, quantum numbers are unintuitive compared to the classic continuous world. But it is precisely the essence of quantum mechanics that certain values ​​only occur exactly and in stages / discrete. The quantum numbers then represent the independently measurable eigenvalues ​​of the operators.

In addition to atomic physics, quantum numbers are also of great importance in the subatomic physics of particle physics. There they serve to identify the nuclei and particles as well as to describe the transitions between them.

Bound electron in the hydrogen atom

The eigen-states of the bound electron and its wave function in the hydrogen atom are described by four quantum numbers:

Principal quantum number

In the shell model, the principal quantum number n describes the shell on which the electron is located. It denotes the basic energy level and can assume any natural numbers greater than zero:

This corresponds to ever higher excitations, with a very large n one speaks of Rydberg atoms. The energy level results from the principal quantum number with:

.

for the hydrogen atom.

Minor quantum number

The secondary quantum number l or also angular momentum quantum number l characterizes the shape of the orbital in an atom. It can take on 0 as well as any natural numbers, but must in any case be smaller than n:

The name "angular momentum quantum number" is historical and goes back to the idea that this quantum number describes the angular momentum of the electron moving around the atomic nucleus. See Bohr-Sommerfeld's atomic model. At the same time is the eigenvalue of the angular momentum operatorL.2.

Magnetic quantum number of angular momentum

The magnetic quantum number of the angular momentum, also called azimuthal quantum number, is with ml and describes the spatial orientation of the electron orbital angular momentum. In terms of amount, it must not be greater than the secondary quantum number l, but it can also assume negative values:

It is called magnetic quantum number because the additional potential energy in a magnetic field in the z-direction (normal Zeeman effect) depends on it (at m = 0 no z component, i.e. no additional energy; at m = l only z-component, i.e. maximum additional energy).

Spin quantum number

Main Products:Spin

The electron's spin quantum number s describes the orientation of the electron's spin. It is half-integer: There are only two options for projecting the spin in the z direction:

More quantum numbers

Total angular momentum quantum number

The total angular momentum quantum number describes the total angular momentum of an electron in which (clearly) the spin couples with the angular momentum and a differentiation between the angular momentum is no longer possible.

Nuclear spin quantum number

Main Products:Nuclear spin

The nuclear spin quantum number (also called nuclear spin or direction quantum number) describes the angular momentum of atomic nuclei. It is made up of the spin of the individual neutrons and protons and can therefore assume positive integer or half-integer values.

Multi-electron systems

In contrast to the hydrogen atom, the shells of other atoms consist of several electrons that influence each other. Nevertheless, one can often approximate their state by the above quantum numbers; In order to distinguish such systems from one-electron systems, however, the quantum numbers are then written in capital letters. E.g. S then describes the total spin of all electrons.

It should be noted, however, that electrons are subject to the Pauli principle because they are fermions: No two electrons may have the same quantum number.

See also:

literature

  • Hook, wolf: Atomic and Quantum Physics. 8th edition. Springer-Verlag, Berlin Heidelberg New York 2004, ISBN 3-540-02621-5

Category: quantum physics