Chromium ($\mathrm{3d^5\,4s^1}$) and copper ($\mathrm{3d^{10}\,4s^1}$) are fairly well-known exceptions to the aufbau principle, often attributed to the stability of the half- or fully-filled 3d subshell (as discussed in this prior question).
However, what experimental evidence is there for this? Is there a spectroscopic method (for example) which can be used to probe electronic configurations?
X-ray Photoelectron Spectroscopy (XPS) can be used to analyze 3d and 4s orbital energies of these elements. This unique behavior comes from the Aufbau principle, which explains why one electron moves to the d-orbital to fill half of the shell or total of the shell.
I used XPS for my previous research with elemental analysis (i.e. ratio of elements and which oxidation state they are in). I am not an expert in this device but comparing metallic copper's 3d shell binding energy with a different element (let's say Zn) would show that their B.E.'s are pretty close. To the best of my knowledge, lower atomic numbered elements in the 3$^{rd}$ row would not show any 3d peak due to very low B.E. (this is the outermost shell).
I don't know if that is the answer but XPS is a strong candidate for demonstrating this phenomena experimentally.
