(a) Two types of nodes occur in atomic orbitals: spherical surfaces and planes. Examine the nodes in 2s, 2p, and 3p orbitals, and show that they agree with the following statements:

1. An orbital of principal quantum number n has n - 1 nodes.

2. The value of ml gives the number of planar nodes.

(b) How many spherical nodes does a 5s orbital have? A 3d orbital? How many nodes of all types does a 3d orbital have?