Question

How would you describe the shapes and relative energies of the s,p,d, and f atomic orbitals?

Answer 1

Shapes are described below, the energies are on average in increasing order in your question, for the same `n`.

Explanation:

Energies of valence orbitals can be found here (Appendix B.9):

http://media.pearsoncmg.com/bc/bc_0media_chem/adv_chem/pdf/11054_appB_ts.pdf

The first five are `1s, 2s, 2p, 3s, 3p`. The remaining energy orderings vary depending on the atom. For `"Ca"`, the `4s` is higher in energy than the `3d`. For the remaining 1st row transition metals, the `3d` is higher in energy than the `4s`.

What we can say for sure is, though,

`E_(ns) < E_(np) < E_(nd) < E_(nf)`.

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The `ns` subshell has a spherelike shape, and on average, lower energy than the rest of the subshells on the same quantum level `n`.

The `np` subshell has two lobes opposite the origin, and on average has more energy than a `ns` subshell since it has one more angular node, and thus `np` electrons are less core-like (and further away from the nucleus).

`nd` orbitals have five spatial orientations:

Wikipedia

`nf` orbitals have seven spatial orientations:

TFChem