# What's the difference between radial probability and probability density?

I understand that radial probability is the probability of finding an electron at some distance from nucleus in a shell. But what does that exactly mean? What does it tell us about the atom and electrons?

Knowing the radial probability of finding an electron as a function of distance from the nucleus tells you a lot about the atom. For instance this electron density can be used to calculate the potential energy and to get an idea about the shell structure. You can estimate many different properties like cohesive energy, band gap, optical properties etc. Take a look on the Thomas$-$Fermi theory, the Hartree$-$Fock method or Density Functional Theory (DFT) to get an idea.