An octahedral complex [M(H₂O)₆]²⁺ absorbs light at a wavelength of 400 nm for its d-d transition. The absorption wavelength for the corresponding tetrahedral complex [M(H₂O)₄]²⁺ with the same metal ion is ________ nm .

Step-by-step solution

The crystal field splitting energy is inversely proportional to the wavelength of absorbed light, = hc . For the octahedral complex: _o = hc _o For the tetrahedral complex: _t = hc _t The relationship between tetrahedral and octahedral splitting energies is: _t = 4 9 _o Substituting the wavelength expressions: hc _t = 4 9 ( hc _o ) 1 _t = 4 9 _o _t = 9 4 _o Given _o = 400 nm : _t = 9 4 400 = 900 nm . Answer: 900