(6-10)   Here are the radial distribution functions for the 2s and 2p orbitals. 

①  If we are interested in the question "what's the probability of finding the particle at a radius close to r ?", why do we plot - as has been done here - r2ψradial2 , rather than just ψradial2 ? 

②  We have said that the "outer wall" of the spherical box surrounding the nucleus is at r = ∞ .  However the value of these radial functions is already approaching zero at around r = 5 x 10-10  m. Why does this happen?

③ How many nodes, in total, does each of these two types of orbital have ?

④ Solution of the the Schrödinger equation reveals that in a hydrogen atom, where there is just one electron, the energy of that electron is the same whether it is in a 2s or a 2p orbital (actually this is not completely true but the difference is very small and explaining it requires a deeper level of theory). 

Looking at the picture, you can see that the most probable distance from the nucleus is greater in a 2s orbital than it is in a 2p orbital. If you were to calculate the mean distance, this is also bigger for 2s. How are we going to reconcile this  with the equality of their energies?

⑤  In atoms with multiple electrons, the energy of an electron in a 2s orbital is significantly lower than in a 2p orbital. Chemists attribute this to "shielding" which, in essence, means repulsion by other electrons which are, on average, closer to the nucleus. This opposes the attraction to the nucleus and raises the potential energy. Shielding does this more effectively to p-orbitals than s-orbitals, hence the higher energy of an electron in 2p than in 2s, in a multielectron atom. Looking at the picture, suggest why this is so.