The value of m is limited by angular quantum number L. For a given value of L, m∈{m|m∈Z and |m|≤l} are both m= -l, ...,-2,-1,0+1,+2 ...+2. These values mean that there are 2l+ 1 orientations in the sublayer with angular quantum number L, and each orientation is equivalent to an "atomic orbit".

The magnetic quantum number represents the orbit (orbital direction) of each sublayer. Several orbits in the same sublayer (with the same L value) have different orientations to the nucleus. The magnetic quantum number Me describes the extension direction of atomic orbit or electron cloud in space.

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The history of quantum number research;

According to the principle of quantum mechanics, the motion, state and angular momentum of electrons outside the nucleus of an atom are not continuously changing, but jumping, that is, quantized. Quantum numbers include principal quantum number, angular quantum number, magnetic quantum numbers and spin quantum numbers.

Traditionally, it is called the principal quantum number (n= 1, 2, 3, 4 ...), which represents the eigenvalue of H after J is removed. So this number depends on the distance between the electron and the nucleus (that is, the radius coordinate r). The average distance will increase with n, so quantum states with different quantum numbers will be said to belong to different electron layers. Angular quantum number (L = 0, 1...n- 1) (also called azimuth quantum number or orbital quantum number) expresses orbital angular momentum through a relation.

In chemistry, this quantum number is very important because it shows the shape of the orbit and has a great influence on the chemical bond and bond angle. Sometimes, different angular quantum number orbits have different codes. An orbit with l=0 is called an S orbit, an orbit with l= 1 is called a P orbit, an orbit with l=2 is called a D orbit, and an orbit with l=3 is called an F orbit.

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