Benzophenone Ketyl color origin I was recently preparing the benzophenone ketyl radical by reacting it with sodium in toluene. Although this compound is really well known and it seems somewhat obvious and accepted in literature that the radical causes a color I am still unable to find anything on the actual transition. There are some luminescence experiments but at least to my research there doesn't seem to be a good explanation on the actual color. 

My suggestion would be that perhaps occupying the former LUMO of the benzophenone to generate a SOMO causes the orbital to shift in energy. I always confuse when something is stabilized or destabilized but since it seems to be in interaction with the two benzene rings I'd suggest that by occupying the orbital you can also lower it in energy a bit and thus promote the excitation of a former HOMO electron into the singly occupied SOMO with visible light. 

According to what I found there are various mechanisms depending on the environment around the radical orbital how it can stabilize itself and thus lower the gap between the two orbitals (former HOMO and new SOMO).
TL;DR: The primary transition responsible for color is apparently the ${\pi{-}\pi}^*$ transition of the conjugated ketyl radical anion. This absorbs usually around the green to orange portions of the visible spectrum, leaving behind the purple-blue, and sometimes green color.

Original answer (background info):
According to Wikipedia/Benzophenone, the ketyl radical is formed by first, transition of the ketone from a singlet (double bond) to a triplet (diradical) state, and then abstraction of an electron from a donor to form the ketyl radical anion.
As I understand, only the radical anion is colorful. Both ref 1 and Wikipedia/Ketyl indicate that color disappears if the radical anion is allowed to oxidize (back to the ketone, which should be in equilibrium with the diradical). So my guess is, when an extra electron is added to the triplet state, this enables new electronic transitions that produce color.
These two sources also indicate both solvent and substituent effects: In the Wikipedia article, the solvent is toluene, and color is deep blue for benzophenone. In the paper, the solvent is isopropyl alcohol, and color is greenish-blue for benzophenone, and varies from blue to green depending on substituents. This also suggests that conjugation plays an effect, since the substituents can directly affect only the phenyls. But this, in turn, affects the energy levels of the double bond.

Edit:
A Google search for &quot;benzophenone ketyl spectrum&quot; (including the image search) gives several results of varying relevance, such as refs 2-4. In particular, from ref 2 (dealing with uranium ketyl radicals):

The electronic absorption spectrum of 2 in toluene features an intense absorption band ($\lambda_\text{max} = \pu{562 nm}$, $\epsilon = \pu{5680 M^{-1} cm^{-1}}$) in the visible region (Figure 8, top). This absorption gives rise to the ketyl complex’s distinctive and intense purple color and is assigned to the ${\pi{-}\pi}^*$ transition of a highly conjugated ketyl system. The transition energy of $\pu{562 nm}$ is blue-shifted from that of the sodium benzophenone ketyl radical, which exhibits the ${\pi{-}\pi}^*$ transition at $\pu{618 nm}$.

Ref 3 talks about $D_1 \leftarrow D_0$ and subsequent $D_n \leftarrow D_1$ transitions, and provides an energy level diagram. I assume $D_n$ refers to the doublet states that form upon abstraction of a hydrogen by (or addition of an electron to) the triplet diradical.
Finally, ref 4 adds:

Bzp is known to have a high ISC quantum yield following UV excitation, but until recently the mechanism of population of the lowest triplet excited state ($T_1$) after photoexciting to its $S_1$ (${nπ}^*$) state remained uncertain. ... These investigations indicate that the dominant pathway involves fast ISC from $S_1$ to $T_2$ (${\pi\pi}^*$) as an intermediate state, with the subsequent rate of population of the lowest vibrational levels of $T_1$ controlled by the time scale for dissipation of excess vibrational energy to the solvent bath after internal conversion (IC) from $T_2$.

(Bzp = benzophenone, ISC = intersystem crossing). It then proceeds to discuss these transitions in more detail.


J. Am. Chem. Soc. 1933, 55 (1), 391–395; doi:10.1021/ja01328a057
J. Am. Chem. Soc. 2008, 130 (20), 6567–6576; doi:10.1021/ja801007q
J. Phys. Chem. A 2004, 108 (40), 8147–8150; doi:10.1021/jp047058a
J. Am. Chem. Soc. 2019, 141 (38), 15222–15229; doi:10.1021/jacs.9b07047