If [Cu(H₂O)₄]²⁺ absorbs a light of wavelength 600 nm for d-d transition, then the value of octahedral crystal field splitting energy for [Cu(H₂O)₆]²⁺ will be ____________ × 10⁻²¹ J. [Nearest Integer]
(Given : h = 6.63 × 10⁻³⁴ Js and c = 3.08 × 10⁸ ms⁻¹)

Solution

Chemistry ma’am · 4 steps

The 600 nm photon gives you the tetrahedral splitting. Scale it up by 9/4 to get the octahedral one.

1. Energy absorbed. The d-d transition absorbs one photon, so its energy equals the splitting of the four-coordinate complex: Δₜ = hc/λ. Use c exactly as given, 3.08 × 10⁸ m s⁻¹.
2. Put in numbers. Δₜ = (6.63 × 10⁻³⁴ × 3.08 × 10⁸)/(600 × 10⁻⁹) = (20.42 × 10⁻²⁶)/(6 × 10⁻⁷) = 3.403 × 10⁻¹⁹ J.
3. Tetrahedral to octahedral. The question treats the four-coordinate complex as tetrahedral. For the same metal ion and ligand, Δₜ = 4/9Δₒ, so Δₒ = 9/4Δₜ.

   Δₒ = 9/4 × 3.403 × 10⁻¹⁹ J = 7.658 × 10⁻¹⁹ J

4. So. Δₒ = 765.8 × 10⁻²¹ J, which rounds to 766.

The common slip: 340. Stopping at hc/λ gives 340, which is the tetrahedral splitting Δₜ, not Δₒ. Multiply by 9/4 to reach the octahedral value.

The idea to keep. The absorbed photon's energy hc/λ is the splitting of that complex itself. To switch between geometries, use Δₜ = 4/9Δₒ for the same metal ion and ligand.

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