For the RDF, we take the square of the radial component multiplied by 4pi r2 (the surface area of a sphere) and this gives us the probability density of finding an electron r distance away. Whats the point in multiplying it by r2?
The Attempt at a Solution
I feel that when I just square the radial component we would get the probability density of finding an electron r distance away. Since the radial component already takes into account the distance from the nucleus (r), should it's squared value should tell us the probability density of finding an electron at a certain distance of r. Similar to how the full wavefunction squared would give us the probability density of finding the electron within a volume stipulated by r, theta, and phi, I feel like squaring the radial component alone would achieve the RDF.
So I can't wrap my head around the idea of multiplying it by the area of the sphere at r distance away as well.
I am a first year chemistry student learning about the Schrodinger's equation for the first time so I apologize if I am unclear about the topic.