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

Jul 3, 2017

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):

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

What we can say for sure is, though,

${E}_{n s} < {E}_{n p} < {E}_{n d} < {E}_{n f}$.

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

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

$n d$ orbitals have five spatial orientations:

$n f$ orbitals have seven spatial orientations: