Question

What is the relation between the radial part of the wave function and number of radial nodes?

Answer 1

For the 3s orbital, the curve has zero probability at 2 points; which is consistent with the n-l-1 for the 3s orbital 3-0-1=2 radial nodes. To separate the wavefunction into a radial part and an angular part, the system needs to be spherically symmetric. For an atom this is the case but a molecule can never be.