what is radial probability function? Explain its significance with respect to s and p orbital.
Dear student!
The radial probability function is defined as the probability of finding an electron at a distance r from the nucleus in the orbital with quantum numbers n and l . It is denoted by P(nl) and is related to the radial wave function by the given relationship:
Pnl (r) = 4πr2 R2
Where the factor 4πr2 arises because the radial distribution function refers to the probability of finding an electron not at a specific point in space (i.e Ψ2 )on a spherical shell of area 4πr2, at a distance r from the nucleus.
In case of s,p orbitals etc, the radial probability function applies a big role as the maxima of the radial probability function describes the stability and penetration of an orbital of a specific shell as for example:
he intensity of maxima in the radial probability function for an orbital at a radial distance of lower orbital is in the order of s>p>d>f
So, for same principal quantum number, the stability and shielding both follows the order as : s>p>d>f
The radial probability function is defined as the probability of finding an electron at a distance r from the nucleus in the orbital with quantum numbers n and l . It is denoted by P(nl) and is related to the radial wave function by the given relationship:
Pnl (r) = 4πr2 R2
Where the factor 4πr2 arises because the radial distribution function refers to the probability of finding an electron not at a specific point in space (i.e Ψ2 )on a spherical shell of area 4πr2, at a distance r from the nucleus.
In case of s,p orbitals etc, the radial probability function applies a big role as the maxima of the radial probability function describes the stability and penetration of an orbital of a specific shell as for example:
he intensity of maxima in the radial probability function for an orbital at a radial distance of lower orbital is in the order of s>p>d>f
So, for same principal quantum number, the stability and shielding both follows the order as : s>p>d>f