what is radial probability function? Explain its significance with respect to s and p orbital.

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:

P

_{nl}(r) = 4πr

^{2}R

^{2}

Where the factor 4πr

^{2}arises because the radial distribution function refers to the probability of finding an electron not at a specific point in space (i.e Ψ

^{2})on a spherical shell of area 4πr

^{2}, 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

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