A d1 octahedral complex is found to absorb visible light, with the absorption maximum occcurring at 523 nm.
a) Calculate the crystal-field splitting energy, Δ , in kJ/mol.
To calculate the crystal-field splitting energy (Δ) in kJ/mol, we need to use the relationship between the wavelength of light (λ) and the energy of light (E).
The energy of light can be calculated using the equation:
E = hc/λ
Where:
E = energy of light (in joules, J)
h = Planck's constant (6.626 x 10^-34 J∙s)
c = speed of light (2.998 x 10^8 m/s)
λ = wavelength of light (in meters, m)
To convert the energy from joules to kJ/mol, we need to divide the energy by Avogadro's number (6.022 x 10^23).
So, let's calculate the energy of light first:
E = (6.626 x 10^-34 J∙s * 2.998 x 10^8 m/s) / (523 x 10^-9 m)
E ≈ 3.794 x 10^-19 J
Next, convert the energy from joules to kJ/mol:
E = 3.794 x 10^-19 J / (6.022 x 10^23)
E ≈ 0.631 kJ/mol
Therefore, the crystal-field splitting energy (Δ) in kJ/mol is approximately 0.631 kJ/mol.