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(I haven't been here for a long time, so tell me if my formatting is fine)

Given

The $\ce{[Ni(H2O)6]^2+}$ complex appears green in solution from the transmitted light. Estimate the wavelength of maximum absorption, and also the crystal field splitting $Δ_0$.

I got 1.59ev for the CFS, but I want to verify if I'm doing this right.

I wasn't sure if I also need to know the wavelengths of light and spin pairing energy for this problem. So I just looked up the average wavelength of red light (650nm) and plugged it in (and ignored spin pairing energy since my prof never talked about it)

My Method

Since H20 isn't charged, so Ni is 2+ to make this complex 2+. Since $\ce{Ni^2+}$ is $[Ar]3d^8$, and water makes a weak ligand field, I basically did Crystal Field method and filled the bottom row (t2g) with 6 electrons and put the remaining 2 electrons in eg.

I then used stablization energy: $ΔE = -6(2/5)Δ_0+2(3/5)Δ_0=-6/5Δ_0$

And then $ΔE = hv = hc/λ= 6/5Δ_0$ (I think I can exclude that negative sign since I'm just finding the splitting)

to get $Δ_0 = 5hc/(6(650nm)) = 1.59ev $

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    $\begingroup$ Absorption of a photon (loosely speaking) causes the transition $\mathrm{t_{2g} \to \mathrm{e_g}}$. The energy needed for this is (by definition) exactly $\Delta_O$, which doesn't actually have anything to do with the CFSE or the electron configuration, so you've gone one step too far. $\endgroup$ – orthocresol Nov 30 '19 at 23:43

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