Radial probability distribution plot

In a two-dimensional rectangular coordinate system, the image of a single variable function can be drawn, and what is obtained is a curve; in a three-dimensional rectangular coordinate system, the image of a function of two variables can be drawn, and the obtained surface is a curved surface
.

In the three-dimensional rectangular coordinate system, the image of the wave function Ψ(x, y, z) with three variables cannot be drawn
.

1.
Radial probability distribution plot

From Figure 5-4, we can understand the changing trend of |Ψ| ² -r
.

If we consider the variation of the probability of electrons in a thin-layer spherical shell per unit thickness with r, the probability that the thickness of the thin-layer spherical shell at the distance r from the core is △r can be found (Figure 5-6)
.

Figure 5-6 Image of 1s electron

(a)|R| ² changes with r; (b) electron cloud: (c) spherical shells of unit thickness with unequal radii

The area of ​​the sphere at the distance r from the core is 4πr ² , and the volume of the thin spherical shell is approximately 4πr ² △r
.

w=4πr ² △r|R| ²

The probability of electrons appearing in unit spherical shell thickness is

D(r) is called the radial distribution function, which represents the probability of electrons appearing in a spherical shell of unit thickness from the core r
.

According to the radial probability distribution diagram, 1s has 1 probability peak, 2s has 2 probability peaks.

Figure 5-7 Radial probability distribution diagram

There is a nodal plane with a probability density of 0 between the two peaks, and the number of nodal planes with a probability density of 0 for each state of electron movement is

N _{section surface} = nl-1