Finding the stable 4f ions

You will write four small functions about the lanthanoid ions. They count the 4f electrons of an ion, the unpaired electrons, the spin-only moment, and then list the charges that leave an empty, half-full or full 4f subshell.

The idea. The ion $\text{Ln}^{q+}$ of the element with atomic number $Z$ has $(Z - 57) + (3 - q)$ electrons in 4f. Unpaired electrons: $f$ up to 7, then $14 - f$. A count of 0, 7 or 14 is a stable subshell.

Your tasks.

1. Complete f_electrons(z, charge) so that it returns the number of 4f electrons.
2. Complete unpaired(f) so that it returns the number of unpaired electrons.
3. Complete spin_only(u) so that it returns the moment in BM.
4. Complete stable_charges(z) so that it returns the list of charges among 2, 3 and 4 for which the ion has 0, 7 or 14 electrons in 4f.