The complex ion, [ni(nh3)6] 2+, has a maximum absorption near 580 nm. calculate the crystal field splitting energy (in kj/mol) for this ion. 292 kj/mol 485 kj/mol 206 kj/mol 343 kj/mol 114 kj/mol

In given data:
maximum absorption wavelength λ = 580 nm = 580 x 10⁻⁹ m
write the equation to find the crystal field splitting energy:
E = hC / λ 
Here, E is the crystal field splitting energy, h = 6.63 x 10⁻³⁴ J.sec is Planck's constant and C = 3 x 10⁸ m/sec is speed of light. 
substitute in the equation above:
E = (6.64 x 10⁻³⁴ x 3 x 10⁸) / (580 x 10⁻⁹) = 3.43 x 10⁻¹⁹J
This crystal field splitting energy is for 1 ion.
Number of atoms in one mole, NA = 6.023 x 10²³ 
to calculate the crystal field splitting energy for one mole:
E(total) = E x NA
             = (3.43 x 10⁻¹⁹) x (6.023 x 10²³) = 206 kJ/ mole