angular node!! why the angular momentum of electron in the ground state is zero?? (an s-electron) And why it has angular momentum when there is a node?? And pls give some info on what is a Radial node and what is an angular node and their contributions to the energy of electrons??
That is what comes out of the Schrodinger equation. It is the solution with the lowest value of [itex]n[/itex], and nature happens to take advantage of that lowest energy solution. I am not quite sure of what you are looking for here. Are you asking why a function that has at least one zero can be an eigenstate of the angular momentum operator? A radial node occurs when the radial part of the wavefunction vanishes, and an angular node occurs when the angular part vanishes. As far as the connection of nodes to energy, how about looking at some specific wavefunctions? Note the number of each type of node, and note the energy.
This goes back to Noether's Theorem. The breaking of continuous rotational symmetry is associated with the addition of angular momentum. What's easier to see is (the converse, namely) that if you have no angular nodes, you must retain spherical symmetry; in which case there would be no "special" direction along which to orient an angular momentum vector.