Integral of RDF over r : ∫r2·|R(r)|2dr
The electron must be somewhere around the nuclear, so the integration of the radial distribution function (RDF) from the nuclear to infinity should be 1, which means:
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Radial probability, also known as radial distribution function (RDF), is the probability of finding the electron within an infinitely thin shell of sphere with radius of r and nucleus as the center. The area of the sphere with radius r is 4πr2, so the probability within that spherical shell is 4πr2 · |ψ|2. As the value of RDF only depends on r, it can be found by only evaluating the radial part of the wave function. RDF is given by r2·|R(r)|2. Please note that 4π is dropped here so that RDF integrates to 1 over all distance r.
Select “Hydrogen” to view orbitals up to n=8. Select any other element in the first six periods to view the occupied atomic orbitals, whose radial wavefunction is approximated by hydrogenenic wavefunction with element- and orbital-dependent effective nuclear charge (Zeff).
The electron must be somewhere around the nuclear, so the integration of the radial distribution function (RDF) from the nuclear to infinity should be 1, which means:
.
Radial wave function R(r) is a separable part of the Ψ (r, ѳ, φ) that only depends on the distance r from the nucleus. It describes the wave-like property of the electron along r.
The quantity of R(r)·R(r) gives the radial probability density of the electron --the probability for the electron to be found at a point with a distance from the nucleus is r.