9. Quantum Mechanics

Which atomic orbital has the fewest angular nodes?  

Which atomic orbital has the greatest number of radial nodes?

With reference to the figure below, what is the relationship between the number of nodes in an s orbital and the value of the principal quantum number?

If you were to plot all the points that lie on the node of the 2s orbital wave function, what shape would you obtain: a set of isolated points, a plane, or a sphere?

a. How many radial nodes are there in the 4s orbital of the hydrogen atom?

b. How many nodal planes are there in a 2𝑝𝑥 orbital of the hydrogen atom?

c. Is the most probable distance from the nucleus of an electron in a 2s orbital larger or smaller than it would be for an electron in a 3s orbital?

d. For the hydrogen atom, list the following orbitals in order of increasing energy (that is, most stable ones first): 4f, 6s, 3d, 1s, 2p.