The principal quantum number n and angular quantum number l in Schrodinger equation

5.
2.
2 Four quantum numbers

When solving Schrodinger's equation, in order to make the equation have a reasonable solution, three parameters n, l, m are introduced.
These parameters can only take certain specific values ​​according to regulations, so they are called quantum numbers
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1.
The principal quantum number n

n is called the principal quantum number, and its values ​​are positive integers 1, 2, 3, 4.
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, and can be represented by the symbols K, L, M, N,.
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in order in spectroscopy
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(1) The size of n indicates the number of layers of electrons in the atom, that is, the distance between the electron (the orbital) and the nucleus
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n=1, which means the first layer (K ​​layer); n=2, which means the second layer (L layer); the larger the n, the farther the average distance between the electrons and the nucleus

(2) The size of n represents the energy level of the electron and atomic orbital
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The larger the n, the farther away from the nucleus, the higher the energy of the electrons and orbits

Units of energy eV (electron volts),.
1 eV = 1.

The larger the n, the higher the energy.
When n→∞, the electron has the highest energy (E=0), which is a free electron
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Due to the limitation of the value of n, the energy E is also quantized

2.
Angular quantum number l

1 azimuthal quantum number is called, the value is 0,1,2,3 .
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, (n-1) , corresponding to the spectroscopic symbol S, P, D, F, G, .
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The value of l is limited by the value of n.

(1) The angular quantum number l determines the shape of the atomic orbital
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The s orbital is spherical, the p orbital is dumbbell-shaped, and the d orbital is petal-shaped, as shown in Figure 5-3

Figure 5-3 Several shapes of atomic orbitals

(2) The angular quantum number l determines the number of sublayers (or layers) in the same electronic layer
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For example, when n=1, then l=0, and there is only one sublayer of s orbital; when n=2, then l=0 and 1, there are two sublayers of s orbital and p orbital; when n=3, then l= 0, 1, 2, there are three sublayers: s orbit, p orbit, and d orbit

(3) For multi-electron atoms, the energy of extranuclear electrons not only depends on the main quantum number n, but also depends on the angular quantum number l

E _4s <E _4p <E _4d <E _4f

(4) The angular quantum number l determines the size of the orbital angular momentum of the electron moving around the nucleus, and the modulus of the orbital angular momentum is

It can be seen that the angular momentum of the orbit is also quantized

Related link: Schrodinger equation