Can carbon have electrons in a 5d orbital? [closed]

Question

(a) Sketch the radial probability distribution for a 5d orbital in a carbon atom. You should label the axes, but do not need to include numbers. Use arrows to indicate the radial nodes.

(b) Label the most probable radius, $r_\mathrm{mp},$ on your 5d radial probability distribution with a *.

The question asks about a $\mathrm{5d}$ orbital in a carbon atom, but to my understanding a ground-state carbon atom should have a configuration of $(\mathrm{1s})^2 (\mathrm{2s})^2 (\mathrm{2p}_x)^1 (\mathrm{2p}_y)^1,$ and no electrons in a $\mathrm{5d}$ orbital.

I understand why there would be two radial nodes $(n - l - 1 = 5 - 2 - 1),$ but shouldn't that be irrelevant because a carbon atom doesn't have electrons in the 5d orbital? Or maybe I am missing something more fundamental and it is still possible for a ground-state carbon to have electrons in $\mathrm{5d}?$ Any suggestions are appreciated.

Answer 1

Empty orbitals are still orbitals, in meaning of the wave functions, allowed quantum states of electrons and respective electron occurence probabilities.

It is true that at the carbon atom ground state, quantum states with $n>2$ are not occupied. But it could happen 5d orbital is occupied in high temperature plasma or by non thermal high energy excitation ( like photons with energies little below the carbon ionization energy), as an electron in carbon atom or ion can get excited to 5d orbital.

There are known Rydberg atoms with very high principal quantum numbers, e.g. $\ce{H}$ atom with $n=137$ has the size about $\pu{0.001 mm}$ and $\ce{K}$ atom with $n=600$ has size almost $\pu{0.1 mm}$.