[Ti(H₂O)₆]³⁺ absorbs light of wavelength 498 nm during a d - d transition. The octahedral splitting energy for the above complex is ____________ × 10⁻¹⁹ J. (Round off to the Nearest Integer). h = 6.626 × 10⁻³⁴ Js; c = 3 × 10⁸ ms⁻¹

Solution

Chemistry ma’am · 3 steps

For a d¹ ion the one absorbed photon carries exactly Δₒ, so just find its energy from hc/λ.

1. Why one photon. Ti³⁺ is d¹, so its single electron sits in t_(2g). Absorbing light lifts it to e_g, and the photon's energy equals the gap Δₒ.

   Δₒ = hc/λ = (6.626 × 10⁻³⁴ × 3 × 10⁸)/(498 × 10⁻⁹)

2. Put in numbers. The top is 1.9878 × 10⁻²⁵ J m and the bottom is 4.98 × 10⁻⁷ m. Dividing gives Δₒ = 3.99 × 10⁻¹⁹ J.
3. So. Δₒ ≈ 3.99 × 10⁻¹⁹ J per ion, which rounds to 4.

The idea to keep. Colour of a d¹ complex gives Δₒ directly: Δₒ = hc/λ per ion. Convert nm to m first, and multiply by N_A only if they ask per mole.

Answer from the NTA final answer key. Solution by PrepWiser.