Which of the following is the correct order for the wavelengths of absorption in the visible region ?

Question

Accepted Answer

The correct order for the wavelengths of absorption in the visible region is given by Option 2: $$ {[Ni(NO_{2})_{6}]}^{4-} < {[Ni(NH_{3})_{6}]}^{2+} < {[Ni(H_{2}O)_{6}]}^{2+} $$ ### Explanation for Option 2: 1. **Crystal Field Theory and Ligand Field Strength:** - The absorption of light in transition metal complexes is influenced by the ligand field strength, which affects the splitting of d-orbitals in the metal ion. - Ligands are arranged in the spectrochemical series based on their ability to split the d-orbitals. Strong field ligands cause a larger splitting, resulting in absorption of shorter wavelengths (higher energy), while weak field ligands cause smaller splitting, resulting in absorption of longer wavelengths (lower energy). 2. **Order of Ligand Field Strength:** - According to the spectrochemical series, the ligands in question can be ordered by their field strength as follows: $$ NO_{2}^{-} > NH_{3} > H_{2}O $$ - This means that $$ NO_{2}^{-} $$ is a stronger field ligand than $$ NH_{3} $$, which in turn is stronger than $$ H_{2}O $$. 3. **Implications for Wavelengths:** - Since $$ NO_{2}^{-} $$ is the strongest field ligand among the three, $$ {[Ni(NO_{2})_{6}]}^{4-} $$ will have the largest d-orbital splitting and thus absorb light at the shortest wavelength. - $$ NH_{3} $$ is a moderate field ligand, so $$ {[Ni(NH_{3})_{6}]}^{2+} $$ will absorb light at a longer wavelength than $$ {[Ni(NO_{2})_{6}]}^{4-} $$ but shorter than $$ {[Ni(H_{2}O)_{6}]}^{2+} $$. - $$ H_{2}O $$ is the weakest field ligand, so $$ {[Ni(H_{2}O)_{6}]}^{2+} $$ will have the smallest d-orbital splitting and absorb light at the longest wavelength. ### Explanation for Why Other Options are Incorrect: 1. **Option 1:** - This option suggests $$ {[Ni(NO_{2})_{6}]}^{4-} $$ absorbs at the longest wavelength, which contradicts the fact that $$ NO_{2}^{-} $$ is the strongest field ligand and should absorb at the shortest wavelength. 2. **Option 3:** - This option incorrectly places $$ {[Ni(NH_{3})_{6}]}^{2+} $$ as absorbing at a longer wavelength than $$ {[Ni(NO_{2})_{6}]}^{4-} $$, which is not consistent with the ligand field strength order. 3. **Option 4:** - This option incorrectly suggests that $$ {[Ni(NO_{2})_{6}]}^{4-} $$ absorbs at the longest wavelength, which is contrary to the known order of ligand field strengths. In conclusion, Option 2 correctly reflects the order of absorption wavelengths based on the ligand field strength, with $$ {[Ni(NO_{2})_{6}]}^{4-} $$ absorbing at the shortest wavelength and $$ {[Ni(H_{2}O)_{6}]}^{2+} $$ at the longest.