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

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Coordination Compounds

If the CFSE of

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

- 96.0 kJ / mol

, this complex will absorb maximum at wavelength ____ nm. (nearest integer)
Assume Planck's constant

(h) = 6.4 \times 1 0^{- 34}

Js Speed of light (c)

= 3.0 \times 1 0^{8} m / s

and Avogadro's constant

(N_{A}) = 6 \times 1 0^{23} / mol

Answer: 480

The

T i^{3 +}

ion is

3 d^{1}

, for which the crystal field stabilization energy is

- 0.4 Δ_{o}

per ion. Equating the given stabilization per ion gives

Δ_{o} = \frac{96 \times 1 0 ^{3}}{0.4 \times 6 \times 1 0 ^{23}} = 4 \times 1 0^{- 19} J

for one ion. The absorbed photon carries this energy, so

λ = \frac{h c}{Δ _{o}} = \frac{( 6.4 \times 1 0 ^{- 34} ) ( 3.0 \times 1 0 ^{8} )}{4 \times 1 0 ^{- 19}} = 4.8 \times 1 0^{- 7} m

. The complex absorbs most strongly at

480 nm

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Integer answer