- #1
kenyanchemist
- 24
- 2
i have a question, why is the plot of r2(Ψ2p)2 not a good representation of the probability of finding an electron at a distance r from the nucleus in a 2p orbital
What do you mean by cancels?vanhees71 said:Well, in spherical coordinates you have
$$\mathrm{d}^3 \vec{x} = \mathrm{d} r \mathrm{d} \vartheta \mathrm{d} \varphi r^2 \sin \vartheta.$$
The wave function squared is the probability distribution. So the probability for finding a particle described by the wave function at a distance ##r## is
$$P(r)=\int_0^{\pi} \mathrm{d} \vartheta \int_0^{2 \pi} \mathrm{d} \varphi \, r^2 \sin \vartheta |\psi(r,\vartheta,\varphi)|^2.$$
Note that sometimes one writes
$$\psi(r, \vartheta,\varphi)=\frac{1}{r} u(r,\vartheta,\varphi),$$
because this ansatz simplifies the solution of the Schrödinger equation in spherical coordinates. In terms of ##u## the factor ##r^2## cancels in the above integral.
$$P(r)=\int_0^{\pi} \mathrm{d} \vartheta \int_0^{2 \pi} \mathrm{d} \varphi \, \sin \vartheta |u(r,\vartheta,\varphi)|^2.$$
Demerits radial distribution functions are mathematical functions used in materials science and chemistry to describe the spatial distribution of defects or imperfections in a crystal lattice. They are commonly used to study the properties of crystalline materials and their defects.
Demerits radial distribution functions are typically calculated using computer simulations or analytical models. The calculations involve analyzing the distance between atoms in a crystal lattice and determining the probability of finding a defect at a specific distance from a reference atom.
Demerits radial distribution functions can provide information about the type, location, and concentration of defects or imperfections in a crystal lattice. They can also help determine the stability and mechanical properties of the material.
X-ray diffraction is often used to study the crystal lattice structure of materials. Demerits radial distribution functions can be used in conjunction with X-ray diffraction data to analyze the presence and characteristics of defects in the crystal lattice.
Demerits radial distribution functions have various applications in materials science, including the study of crystal defects, the design of new materials with specific properties, and the analysis of materials under extreme conditions such as high temperatures or pressures. They are also used in pharmaceutical research to study the structure of drugs and their interactions with biological molecules.