How to Calculate Crystal Field Splitting Energy for an Octahedral Complex Absorbing Light at 497 nm?

To calculate the crystal field splitting energy (Δ) for the octahedral complex, we can use the formula:

Δ = rac{hc}{ ext{wavelength}}

Where:

• h = Planck’s constant = 6.626 x 10^-34 J·s
• c = speed of light = 3.00 x 10⁸ m/s
• wavelength = 497 nm = 497 x 10^-9 m

Now, substituting the values into the formula:

Δ = rac{(6.626 imes 10^{-34} ext{ J·s})(3.00 imes 10^8 ext{ m/s})}{497 imes 10^{-9} ext{ m}} = 3.997 imes 10^{-19} ext{ J}

Now, we need to convert this energy from joules to kilojoules per mole. We use the conversion factor that 1 mole contains Avogadro’s number of particles (approximately 6.022 x 10²³ particles/mole). Thus:

Δ (in kJ/mol) = rac{3.997 imes 10^{-19} ext{ J} imes 6.022 imes 10^{23} ext{ mol}^{-1}}{1000} ext{ kJ}
≈ 241.2 ext{ kJ/mol}

Therefore, the crystal field splitting energy (Δ) for the octahedral complex is approximately 241.2 kJ/mol.