The periodic table of chemical elements was first compiled by Mendeleev in 1869.
Textbooks are marked with valence electrons of atoms, that is, peripheral electrons.
1s( 1) is the arrangement of peripheral electron layers (1 stands for 1 electron layer in brackets), (hydrogen) is an element, and d s f in "5f Φ 6d ΦΦ 7s Φ Φ" stands for different electron sublayers.
Sublayer electron layer
, n, l, m and ms show that Schrodinger equation is the basic equation to describe the motion of microscopic particles. 1927, Austrian physicist Schrodinger extended the wave equation of light to describe the motion law of a single electron in an atom, which is a second-order partial differential equation. When solving the equation, in order to make the solved function have reasonable physical meaning, a set of parameters N, L and M must also be introduced as restrictive conditions. This set of parameters is called quantum number in quantum chemistry. Its value principle is:
N = 1, 2, 3, …, ∞ n is a natural number.
l≤n– 1 l = 0， 1，2，…，(n - 1)
|m| ≤ l m = 0， 1，2，…，l
1, principal quantum number (n)
Describe the distance between the electron and the nucleus, determine the energy level of the atom or determine the orbital energy. Determines the distribution range of orbits or electron clouds. Generally, the greater the value of n, the farther the electron is from the nucleus, and the higher the energy. The dense region or energy state of the electron cloud determined by principal quantum number is called the electron layer (or main layer).
Principal quantum number n = 1, 2, 3, 4, 5, 6, 7, ... (n values in total).
Electron layer symbols k, l, m, n, o, p, q, …
2, angular quantum number (quantum number) (L)
The same electron layer (n) is divided into several electron sublayers (referred to as sublayers for short, sometimes referred to as energy levels) due to different attached quantum numbers (L). L determine the shapes of different atomic orbits in the same electron layer. In a multi-electron atom, it and n together determine the orbital energy.
Attached quantum number l = 0, 1, 2, 3, 4, …, n- 1 (n values can be taken).
Sublayer symbols s, p, d, f, g ...
3, the magnetic quantum number (m)
Determine the extension direction of atomic orbit in space.
M = 0, 1, 2, 3, …, l can take (2l+1) values.
The number of spatial extension directions of S, P, D and F orbits are 1, 3, 5 and 7 (the number of values of m) respectively.
Each value of m represents an electron orbit with a certain spatial direction, and the value of m in the same sublayer L corresponds to different extension directions of the sublayer. Under the condition of no external magnetic field, the energy of the same sublayer is the same, that is, the energy of different orbits with the same N and L is the same, and the orbits with the same energy are called equivalent orbits or degenerate orbits.
N and L determine the energy of electrons, and L determines the momentum of electron motion. Because n and l are quantized, the energy and momentum of electrons are quantized, and m determines the different distribution of the same angular momentum l in space.
The direction of angular momentum is different, the orbital magnetic moment is different, and the interaction with external magnetic field is different. Because the direction of the orbital magnetic moment is quantized, the acting energy of the external magnetic field is quantized, and the additional energy value of M is different, the original 2l+ 1 orbit splits in the external magnetic field, which is called Zeeman effect. M is used to calculate the projection of momentum in the direction of magnetic field under the action of external magnetic field.
4, Ms. Every electron is spinning. When quantum mechanics calculates spin momentum, it takes 1/2, which has two directions. When calculating the external magnetic field, the projection of spin momentum in the magnetic field direction is reduced to 1/2.
According to the Polly exclusion principle, there are no four electrons with the same quantum number in the atom, so the number of electrons that can be accommodated in the same sublayer L is 2(2l+ 1).
2，n，l，j，mj
As can be seen from the above, there are orbital angular momentum and spin angular momentum, so they will produce orbital magnetic moment and spin magnetic moment. Orbital magnetic moment forms a magnetic field in the atomic range, and spin magnetic moment has two different orientations relative to the magnetic field, thus generating different additional energy.
Electron motion: orbital motion+spin motion
The total angular momentum of electrons: J=L+S (vector) shows that the total angular momentum is also quantized.
Quantum mechanics shows that J= radical number j (j+1) h j = | l+-s | s =1/2.
When l=0, it is an S orbital electron, and j= 1/2. The orbital magnetic moment calculated by quantum mechanics is zero, and only the spin magnetic moment exists.
L=0 J=S= root number 3/4h
L= 1, j = 1/2, 3/2 On the p orbit, j has two values.
Similarly, the d orbit is split into j =3/2, 5/2, and the f orbit is split into j =5/2, 7/2. ...
It can be seen from the above that the total angular momentum is related to J. When there is an external magnetic field, the projection of momentum in the magnetic field direction is calculated by mj, and the range of mj is–J, -J+1…,-1/2,1…, J- 1.
If j=l+ 1/2, there are 2l+2 mjs, and if j=l- 1/2, there are 2l mjs.
The steady state of electrons can be expressed by quantum numbers n, l, m and Ms, and the l quantum number of each sublayer is 2(2l+ 1) under the spin condition, or it can be expressed by quantum numbers n, l, j and MJ, and there are 2(2l+ 1) under the spin coupling condition.
When the orbital-spin coupling is not considered, the momentum is determined by L and the direction is determined by M in the external magnetic field. When the orbital-spin coupling is considered, the momentum is determined by J and the direction is determined by mj under the external magnetic field.
After coupling, when there is no external magnetic field, the energy of electrons is expressed as:
E=E(n，l)+δE(j，n，l)
Energy is mainly determined by principal quantum number and angular quantum number. When l=0, the S orbits are not coupled; when δ E = 0, j=l+ 1/2, δ E > 0; when j=l- 1/2, δ E < 0.
Spin coupling is considered in spectral analysis. Except for the S orbit, the P, D and F orbitals are all split into two energy levels, and the energy from low to high is:
s——p 1/2——P3/2——D3/2——D5/2——F5/2——F7/2