You are a scientist investigating complexes of titanium for use as photoactive coatings for selfcleaning windows. These coatings can oxidize organic materials (dirt) upon exposure to light, leaving a clean surface. The excited-state energy must be large to be useful in this application, and you need to calculate the excited-state energy for one of your promising materials. The complex [Ti(OH₂)₆]³⁺ absorbs light of wavelength 510. nm. What is the ligand field splitting in the complex in kilojoules per mole (kJ · mol^–1)?

PLAN Because a photon has energy hv, where h is Planck’s constant and v (nu) is the frequency of the radiation, it can be absorbed if hv = Δ_O. The wavelength, l (lambda), of light is related to the frequency by Eq. 1 of Topic 1A (λ = c/v, where c is the speed of light). Therefore, the wavelength of light absorbed and the ligand field splitting are related by Δ_O = hc/λ. To report the ligand field splitting as a molar energy, multiply this expression by Avogadro’s constant: Δ_O = N_Ahc/λ.