If the CFSE of [ Ti ( H 2 O ) 6 ] 3 + is - 96 . 0 kJ/mol , this complex will absorb maximum at wavelength _________ nm. (nearest integer) Assume Planck's constant ( h ) = 6 . 4 × 10 - 34 J s , Speed of light ( c ) = 3 . 0 × 10 8 m/s and Avogadro

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Solution

Q.
If the CFSE of ${[Ti {(H_{2} O)}_{6}]}^{3 +}$ is $- 96.0$ $kJ/mol,$ this complex will absorb maximum at wavelength _________ nm. (nearest integer) Assume Planck's constant $(h) = 6.4 \times 10^{- 34} J s,$ Speed of light $(c) = 3.0 \times 10^{8} m/s$ and Avogadro's constant $(N_{A}) = 6 \times 10^{23} / mol$ [2023]

Ans.
(480)

${[Ti {(H_{2} O)}_{6}]}^{3 +}$

${Ti}^{3 +} : 3 d^{1} \Rightarrow t_{2 g}^{1, 0, 0} e_{g}^{0, 0}$

$CFSE = [- 0.4 n_{t_{2 g}} + 0.6 n_{e_{g}}] Δ_{o}$

$= \frac{- 96 \times 10^{3}}{6 \times 10^{23}} = - 0.4 Δ_{o}$

$Δ Δ_{o} = \frac{96 \times 10^{3}}{0.4 \times 6 \times 10^{23}} = 4 \times 10^{- 19} J$

$Δ Δ_{o} = \frac{h c}{λ} = 4 \times 10^{- 19} J$

$λ = \frac{6.4 \times 10^{- 34} \times 3 \times 10^{8}}{4 \times 10^{- 19}} = 4.8 \times 10^{- 7} m$

$λ = 480 \times 10^{- 9} m$

$λ = 480 nm$

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