what is the difference between radial function and radial distribution wavefunction??
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The radial probability can be thought as the probability of finding the particle within an interval of length dr at r=r0. So, the radial distribution is a function but the radial probability as described can be calculated by integrating that function from 0 to r0. I'd say the wave function is your ψ.
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An orbital is a mathematical function called a wave function that describes an electron in an atom. The wave functions, ψ, of the atomic orbitals can be expressed as the product of a radial wave function, R and an angular wave function, Y.
- Radial wave functions for a given atom depend only upon the distance, r from the nucleus. Angular wave functions depend only upon direction, and, in effect, describe the shape of an orbital.
ψ = radial function × angular function
= R × Y
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Radial distribution wave function is often useful to know the likelihood of finding the electron in an orbital at any given distance away from the nucleus.
- This enables us to say at what distance from the nucleus the electron is most likely to be found, and also how tightly or loosely the electron is bound in a particular atom.
- This is expressed by the radial distribution function.
- For s-orbitals, the radial distribution function is given by multiplying the electron density by 4πr2.
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